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IIT JEE Super Course in Physics: Mechanics I

Trishna Knowledge Systems

Chapter 2

Motion in One Dimension - all with Video Answers

Educators

Chapter Questions

03:32

Problem 1

A particle travelling along a straight line travels the first $50 \mathrm{~m}$ with a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$, travels at a uniform velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $5 \mathrm{~s}$ and travels at a uniform velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $10 \mathrm{~s}$.
(i) What is the average velocity of the journey?
(ii) If the last part of the journey (during last $10 \mathrm{~s}$ ), was performed at a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ from an initial velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$, what is the average velocity of the journey?

Satpal Satpal
Satpal Satpal
Numerade Educator
03:32

Problem 1

A particle travelling along a straight line travels the first $50 \mathrm{~m}$ with a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$, travels at a uniform velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $5 \mathrm{~s}$ and travels at a uniform velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $10 \mathrm{~s}$.
(i) What is the average velocity of the journey?
(ii) If the last part of the journey (during last $10 \mathrm{~s}$ ), was performed at a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ from an initial velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$, what is the average velocity of the journey?

Satpal Satpal
Satpal Satpal
Numerade Educator
03:32

Problem 2

A particle travelling along a straight line travels the first $50 \mathrm{~m}$ with a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$, travels at a uniform velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$ for the next 5 s and travels at a uniform velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $10 \mathrm{~s}$.
(i) What is the average velocity of the journey?
(ii) If the last part of the journey (during last $10 \mathrm{~s}$ ), was performed at a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ from an initial velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$, what is the average velocity of the journey?

Satpal Satpal
Satpal Satpal
Numerade Educator
03:38

Problem 2

A stone falls from a balloon at a height of $100 \mathrm{~m}$ above ground.
(a) How much time is required for the stone to reach the ground, if
(i) the balloon is ascending uniformly at $5 \mathrm{~m} \mathrm{~s}^{-1}$ ?
(ii) the balloon is descending uniformly at $5 \mathrm{~m} \mathrm{~s}^{-1}$ ?
(iii) the balloon is stationary?
(b) If $\mathrm{t}_{1}, \mathrm{t}_{2}$ and $\mathrm{t}$ are the answers to (i),
(ii) and (iii) respectively, then $\mathrm{t}_{1} \mathrm{t}_{2}=\mathrm{t}^{2}$. Does it hold for any initial height of the balloon and any initial velocity of the balloon? $\left(g=10 m s^{-2}\right)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
09:48

Problem 3

The velocity-time graph of a particle in 1 D motion is given below.
(i) Draw the acceleration-time graph from $\mathrm{t}=0$ to $\mathrm{t}=12 \mathrm{~s}$.
(ii) Find displacement in the interval $\mathrm{t}=3 \mathrm{~s}$ to $\mathrm{t}=6 \mathrm{~s}$.
(iii) Find displacement from $\mathrm{t}=0$ till $\mathrm{t}=12 \mathrm{~s}$.
(iv) Find distance covered from $\mathrm{t}=0$ till $\mathrm{t}=12 \mathrm{~s}$.

Sunil Bidasar
Sunil Bidasar
Numerade Educator
02:40

Problem 4

A car accelerates from rest for a distance $\alpha$ s, after which it decelerates for a distance $\beta$ s and comes to rest in total time t. Find the maximum velocity and the initial acceleration.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:54

Problem 5

A particle starts from rest and travels horizontally with a constant acceleration. At some point it hits a wall where its velocity and acceleration are reversed without any change in their magnitudes. If the particle returns to the initial point, find the ratio of the time taken for the forward and reverse journey.

Satpal Satpal
Satpal Satpal
Numerade Educator
04:10

Problem 6

A train running on a straight track starts from station A, runs with constant acceleration of $0.5 \mathrm{~m} \mathrm{~s}^{-2}$ for $30 \mathrm{~s}$, then maintains uniform speed for some time, applies brake (giving constant retardation) $150 \mathrm{~m}$ ahead of station $\mathrm{B}$ and stops at B. If the total running time was $170 \mathrm{~s}$, calculate the distance between the stations.

Satpal Satpal
Satpal Satpal
Numerade Educator
03:54

Problem 7

From top of a tall building, object A was dropped at $t=0$ and object $B$ was thrown down at $t=2 s$ with a velocity of $40 \mathrm{~m} \mathrm{~s}^{-1}$. From a spot on the ground vertically down, object $\mathrm{C}$ was thrown up at $\mathrm{t}=1 \mathrm{~s}$ with a velocity of $30 \mathrm{~m} \mathrm{~s}^{-1}$. All three objects collide. What was the height of the building? $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:49

Problem 8

A platform starts from rest on the ground and moves up with a constant acceleration of $10 \mathrm{~m} \mathrm{~s}^{-2} .$ If two particles are released from the platform at time $\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ respectively, find the ratio of the time $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ taken by the two particles to hit the ground $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$.

Satpal Satpal
Satpal Satpal
Numerade Educator
03:37

Problem 9

Two particles are projected vertically upwards with speed $20 \mathrm{~m} \mathrm{~s}^{-1}$ and $100 \mathrm{~m} \mathrm{~s}^{-1}$ respectively from the top of a tower. If their times of flight are in the ratio $1: 3$, find the height of the tower $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$.

Satpal Satpal
Satpal Satpal
Numerade Educator
04:11

Problem 10

A boat moves from $\mathrm{P}$ to $\mathrm{Q}$ (downstream) in $2.5 \mathrm{~h}$ and from $\mathrm{Q}$ to $\mathrm{P}$ (upstream) in $5.0 \mathrm{~h}$ respectively, when the engine is producing maximum speed on the boat in each case. If due to increased water flow, the speed of flow of the river gets doubled, how long will it take the boat (moving with maximum possible speed) to move from
(i) P to Q (downstream)?
(ii) Q to P (upstream)?

Satpal Satpal
Satpal Satpal
Numerade Educator
02:17

Problem 11

A ball thrown vertically upwards from level ground is observed twice, at a height H above the ground, within a time interval t. The initial velocity of the ball was
(a) $\sqrt{8 \mathrm{gH}+\mathrm{g}^{2} \mathrm{t}^{2}}$
(b) $\sqrt{8 \mathrm{gH}+\left(\frac{\mathrm{gt}}{2}\right)^{2}}$
(c) $\frac{1}{2} \sqrt{8 \mathrm{gH}+\mathrm{g}^{2} \mathrm{t}^{2}}$
(d) $\sqrt{8 \mathrm{gH}+4 \mathrm{~g}^{2} \mathrm{t}^{2}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:42

Problem 12

Acceleration-time graph of a particle starting from rest and moving along a straight line is as shown. The velocity of the particle after $4 \mathrm{~s}$ is $(\mathrm{in} \mathrm{m} / \mathrm{s})$.
(a) 10
(b) 20
(c) 15
(d) 30

Satpal Satpal
Satpal Satpal
Numerade Educator
01:19

Problem 13

A particle, having an initial velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$ moves along a straight line with a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ for 10
s. Its displacement in the last second is
(a) $25 \mathrm{~m}$
(b) $30 \mathrm{~m}$
(c) $24 \mathrm{~m}$
(d) $27 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:42

Problem 14

A body is thrown up from a tower. If the ratio of distance to displacement is $\mathrm{n}$, the ratio of time for upward and downward motion is
(a) $\frac{1}{\mathrm{n}}$
(b) $\frac{1}{\sqrt{n}}$
(c) $\sqrt{\frac{\mathrm{n}-1}{\mathrm{n}+1}}$
(d) $\sqrt{1-\frac{1}{\mathrm{n}}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:20

Problem 15

Two passenger trains pass (at the same instant) through points A and B, which are $200 \mathrm{~km}$ apart. They run on parallel tracks towards each other at speeds of $60 \mathrm{~km} / \mathrm{h}$ and $45 \mathrm{~km} / \mathrm{h}$ respectively. They will meet in
(a) $2 \frac{1}{2}$ hour
(b) $1 \frac{3}{4}$ hour
(c) $1 \frac{19}{21}$ hour
(d) $1 \frac{16}{21}$ hour

Satpal Satpal
Satpal Satpal
Numerade Educator
01:44

Problem 16

Statement 1 For a particle in $1 \mathrm{D}$ uniformly accelerated motion, if displacement from origin is zero at time $\mathrm{t}=\mathrm{t}_{1}$ and at $\mathrm{t}=\mathrm{t}_{2}$, $\left(\mathrm{t}_{1}, \mathrm{t}_{2} \neq 0\right)$ then $\hat{\mathrm{r}}_{0}=\hat{\mathrm{a}}$ where $\overline{\mathrm{r}}_{0}$ and $\overline{\mathrm{a}}$ are initial position vector and acceleration vector respectively.
and Statement 2 For $1 \mathrm{D}$ motion with constant acceleration, displacement is quadratic in $\mathrm{t}$, $a x^{2}+b x+c=0$ cannot have two positive roots if $a$ and $c$ have opposite signs

Ajay Singhal
Ajay Singhal
Numerade Educator
01:44

Problem 17

Statement 1 If two particles in their vertical motions under gravity, cross each other once, it is quite possible they may cross each other again.
and
Statement 2 : ut $+\frac{1}{2}$ at $^{2}$ can have two roots for a given value of $s$.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:51

Problem 18

Statement 1 If velocity of a particle in 1 D motion increases with time parabolically, then during any given interval of time, it would cover less distance than it would if it had travelled with constant acceleration equal to the average acceleration as per parabolic law.
and
Statement 2 Area under the referred parabola is less than area under the chord.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:23

Problem 19

STATEMETNT - 1 If two cars travel along same straight line in same direction, each with constant acceleration and if the distance between them decreases with time, then they cannot be travelling with same acceleration.
and
Statement 2 Area under relative velocity vs time graph gives relative displacement and slope of the graph gives relative acceleration.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:18

Problem 20

Statement 1 For a particle travelling along a straight line such that velocity increases with time, its average acceleration in any given time interval cannot be more than both its initial and final instantaneous accelerations
and
Statement 2
Average acceleration is ratio of change in velocity to time.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:02

Problem 21

B overtakes A at
(a) $16 \mathrm{~s}$
(b) $12 \mathrm{~s}$
(c) $8 \mathrm{~s}$
(d) $4 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:40

Problem 22

A overtakes $\mathrm{B}$ at
(a) $10 \mathrm{~s}$
(b) $8 \mathrm{~s}$
(c) $12 \mathrm{~s}$
(d) $16 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:04

Problem 23

The initial velocity of $\mathrm{C}$ is
(a) $20 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $30 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $35 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $40 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
04:03

Problem 24

The height of the second drop above the ground is
(a) $\frac{9 \mathrm{~h}}{25}$
(b) $\frac{16 \mathrm{~h}}{25}$
(c) $\frac{4 \mathrm{~h}}{25}$
(d) $\frac{12 \mathrm{~h}}{25}$

Satpal Satpal
Satpal Satpal
Numerade Educator
04:03

Problem 25

The distance between the fourth and second drop is
(a) $\frac{\mathrm{h}}{25}$
(b) $\frac{12 \mathrm{~h}}{25}$
(c) $\frac{7 \mathrm{~h}}{25}$
(d) $\frac{16 \mathrm{~h}}{25}$

Satpal Satpal
Satpal Satpal
Numerade Educator
04:03

Problem 26

The time interval between the release of two successive drops is
(a) $\frac{2}{5} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}$
(b) $\frac{3}{5} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}$
(c) $\frac{4}{5} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}$
(d) $\frac{1}{5} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:45

Problem 27

A body starting from rest, uniformly accelerates for first $10 \mathrm{~s}$ and then uniformly decelerates for next $20 \mathrm{~s}$ and comes to a halt. It covers $300 \mathrm{~m}$ during the whole journey. Then
(a) maximum velocity is $20 \mathrm{~m} \mathrm{~s}^{-1}$
(b) velocity at 5 seconds after start is $10 \mathrm{~m} \mathrm{~s}^{-1}$.
(c) velocity at 5 seconds before stop is $5 \mathrm{~m} \mathrm{~s}^{-1}$.
(d) distance covered in accelerated motion is $200 \mathrm{~m}$.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:36

Problem 28

A body moving with uniform retardation in $+\mathrm{X}$ direction has a velocity $\sqrt{\mathrm{k} \ell}$ at origin and $\sqrt{\ell}$ at a distance $\ell$ from origin.
(a) The time to travel $\ell$ distance from origin is $\mathrm{t}=\frac{2 \sqrt{\ell}}{(\sqrt{\mathrm{k}}+1)}$.
(b) Acceleration $\mathrm{a}=\left(\frac{\mathrm{k}-1}{2}\right)$.
(c) Its velocity at $\frac{\ell}{2}$ is $\sqrt{\frac{\ell(\mathrm{k}+1)}{2}}$.
(d) Its velocity at $\frac{\ell}{2}$ is $\sqrt{\frac{\ell}{2}(\mathrm{k}-1)}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:26

Problem 29

A ball A is dropped from a $180 \mathrm{~m}$ tall tower. After 1 s another ball $\mathrm{B}$ is projected from right below the tower with initial velocity of $25 \mathrm{~m} \mathrm{~s}^{-1}$
(a) B reaches ground earlier than A.
(b) Both reach ground together.
(c) When they meet, their relative velocity is $25 \mathrm{~m} \mathrm{~s}^{-1}$.
(d) When they meet, $\mathrm{v}_{+}>\mathrm{v}_{\mathrm{p}}$ and their velocities will be in same direction.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:22

Problem 30

$\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ are non-zero constants, all greater than zero. The position of a particle in one dimensional motion, at time ' $\mathrm{t}$ ' from start, is represented by (a), (b), (c) and (d) in column I.
Column I
(a) $\mathrm{A}+\mathrm{Bt}+\mathrm{Ct}^{2}$
(b) $\mathrm{Bt}-\mathrm{Ct}^{2}$
(c) $\mathrm{A}-\mathrm{Ct}^{2}$
(d) $\mathrm{Ct}^{2}$
Column II
(p) an accelerating body.
(q) it can be a body moving vertically up.
(r) a body which starts from the origin of the coordinate system.
(s) A body which starts from a point other than the origin.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:34

Problem 31

When a bus takes a hairpin curve on a hill, the motion will be
(a) two dimensional
(b) three dimensional
(c) one or two dimensional
(d) two or three dimensional

Satpal Satpal
Satpal Satpal
Numerade Educator
02:12

Problem 32

A person takes 3 steps forward and 1 step backward, again 3 steps forward and one step backward and so on. Each step is 1 foot long and takes 1 second. The time in which the person falls in a pit 7 feet away from the starting point will be (assume the person cannot stand at the edge of the pit).
(a) $12 \mathrm{~s}$
(b) $11 \mathrm{~s}$
(c) $14 \mathrm{~s}$
(d) $13 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:49

Problem 33

A car takes t second to travel from $\mathrm{A}$ to $\mathrm{B}$. During the first half of the time it travels with a speed $\mathrm{v}_{1}$ and for the second half it travels with a speed $\mathrm{v}_{2}$. The average speed is
(a) $\frac{2 \mathrm{v}_{1} \mathrm{v}_{2}}{\mathrm{v}_{1}+\mathrm{v}_{2}}$
(b) $\frac{\mathrm{v}_{1} \mathrm{v}_{2}}{\mathrm{v}_{1}+\mathrm{v}_{2}}$
(c) $\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}$
(d) $\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{\mathrm{v}_{1} \mathrm{v}_{2}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:47

Problem 34

The position-time graph of a body in uniform motion is as shown. Then,
(a) the body is moving away from the observer.
(b) the body is moving towards the observer.
(c) such a position-time graph is not possible in the case of uniform motion.
(d) the body is moving with decreasing velocity.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:05

Problem 35

The position time graphs of two bodies moving in the same direction are as shown. The ratio of their speeds $\mathrm{v}_{\mathrm{A}}: \mathrm{v}_{\mathrm{B}}$ will be
(a) $3: 1$
(b) $1: 3$
(c) $\sqrt{3}: 1$
(d) $1: \sqrt{3}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:13

Problem 36

A particle moves along a straight line with uniform acceleration and $\mathrm{v}_{1}, \mathrm{v}_{2}$ and $\mathrm{v}_{3}$ denote the average velocities in the three successive intervals of time $\left(0, t_{1}\right),\left(t_{1}, t_{2}\right)$ and $\left(t_{2}, t_{3}\right)$ respectively. Which of the following relations is correct?
(a) $\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right)$
(b) $\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right)$
(c) $\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{1}-\mathrm{t}_{3}\right)$
(d) $\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{2}-\mathrm{t}_{3}\right)$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:49

Problem 37

Which of the following graphs shown in figure represents motion with uniform speed along a straight line? $\mathrm{s} \rightarrow$ displacement
$\mathrm{v} \rightarrow$ velocity

Satpal Satpal
Satpal Satpal
Numerade Educator
02:06

Problem 38

The variation of velocity of a particle moving along a straight line is illustrated in the figure. The distance travelled by the particle in $4 \mathrm{sis}$
(a) $60 \mathrm{~m}$
(b) $55 \mathrm{~m}$
(c) $30 \mathrm{~m}$
(d) $25 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:34

Problem 39

A train $200 \mathrm{~m}$ long passes over a bridge $600 \mathrm{~m}$ long. The time taken by the train to cross the bridge when the train moves with a uniform speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$ is
(a) $100 \mathrm{~s}$
(b) $40 \mathrm{~s}$
(c) $80 \mathrm{~s}$
(d) $60 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:21

Problem 40

A body moves from $A$ to $B$ with a constant speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ and returns from $\mathrm{B}$ to $\mathrm{A}$ with a constant speed of $40 \mathrm{~m}$ $\mathrm{s}^{-1}$. The average speed of the body for the whole journey is
(a) $(80 / 3) \mathrm{m} \mathrm{s}^{-1}$
(b) $30 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $60 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $40 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:56

Problem 41

Which of the following displacement time graphs represents one-dimensional uniform motion?
A.
B.
C.
D.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:33

Problem 42

If a body, starting from rest and moving with constant acceleration, covers $10 \mathrm{~m}$ in the first second, the distance travelled by it in the next second will be
(a) $10 \mathrm{~m}$
(b) $20 \mathrm{~m}$
(c) $30 \mathrm{~m}$
(d) $40 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:18

Problem 43

A car starting from rest and moving on a straight road with constant acceleration, attains a speed of $40 \mathrm{~m} \mathrm{~s}^{-1}$ in $20 \mathrm{~s}$. Its average acceleration is
(a) $0.5 \mathrm{~m} \mathrm{~s}^{2}$
(b) $2 \mathrm{~m} \mathrm{~s}^{-2}$
(c) $4 \mathrm{~m} \mathrm{~s}^{-2}$
(d) $8 \mathrm{~m} \mathrm{~s}^{-2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:33

Problem 44

A body starting from rest and moving along a straight line with uniform acceleration attains a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$ in 2
s. The distance travelled by this body in the first $4 \mathrm{~s}$ of its motion will be
(a) $10 \mathrm{~m}$
(b) $20 \mathrm{~m}$
(c) $30 \mathrm{~m}$
(d) $40 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:04

Problem 45

A bullet hitting a wooden block loses half its velocity when it penetrates $60 \mathrm{~cm}$. If the retardation is uniform, it will come to rest after penetrating a further distance of
(a) $10 \mathrm{~cm}$
(b) $20 \mathrm{~cm}$
(c) $30 \mathrm{~cm}$
(d) $40 \mathrm{~cm}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:17

Problem 46

The velocity-time graph of a body in one dimensional motion is as shown. The distance covered by the body in 10 second is
(a) $25 \mathrm{~m}$
(b) $50 \mathrm{~m}$
(c) $100 \mathrm{~m}$
(d) $150 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:41

Problem 47

In the above question, the distance travelled by the body in the fifth second is
(a) $4 \mathrm{~m}$
(b) $3 \mathrm{~m}$
(c) $9 \mathrm{~m}$
(d) $7 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:49

Problem 48

In Q. No. 46 the distance travelled by the body in the 10 th second is
(a) $1 \mathrm{~m}$
(b) $3 \mathrm{~m}$
(c) $5 \mathrm{~m}$
(d) $7 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:52

Problem 49

The position time graph of a body is as shown. Then the,
(a) body moves with a varying velocity.
(b) body moves with a varying acceleration.
(c) motion is impossible.
(d) body is at rest.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:25

Problem 50

From the given velocity-time graph of a body in 1 D motion, the displacement of the body in $5 \mathrm{~s}$ is
(a) $2 \mathrm{~m}$
(b) $3 \mathrm{~m}$
(c) $4 \mathrm{~m}$
(d) $5 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:52

Problem 51

From the given graph the total distance travelled by the body in $30 \mathrm{~s}$,
(a) $200 \mathrm{~m}$
(b) $250 \mathrm{~m}$
(c) $300 \mathrm{~m}$
(d) $400 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:25

Problem 52

In the above question the distance travelled by the body in the 12 th second will be
(a) $10 \mathrm{~m}$
(b) $20 \mathrm{~m}$
(c) $100 \mathrm{~m}$
(d) $200 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:42

Problem 53

Figure shows a - $\operatorname{tgraph}$ of a body starting from rest. Then the velocity of the body after 2 s is
(a) $5 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $10 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $20 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $15 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:16

Problem 54

In the above case distance travelled by the body in the first 2 s is
(a) $5 \mathrm{~m}$
(b) $10 \mathrm{~m}$
(c) $20 \mathrm{~m}$
(d) $15 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:03

Problem 55

In Q.No. 53 , velocity of the body at the end of $4 \mathrm{~s}$ is
(a) $10 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $7 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $14 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $20 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:06

Problem 56

A body is thrown vertically upward. Which among the following is its velocity time graph?
A.
B.
C.
D

Satpal Satpal
Satpal Satpal
Numerade Educator
01:49

Problem 57

The displacement of a body moving along a straight line is given by $x=\mathrm{pt}^{2}+\mathrm{qt}+\mathrm{r}$ where $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are constants and $\mathrm{t}^{\prime}$ represents time. The acceleration of the body will
(a) remain a constant
(b) decrease
(c) increase
(d) first increase and then decrease

Satpal Satpal
Satpal Satpal
Numerade Educator
01:48

Problem 58

The velocity of a body depends on time according to the equation $\mathrm{v}=20+0.1 \mathrm{t}^{2}$. The body is undergoing
(a) uniform acceleration
(b) non-uniform acceleration
(c) uniform deceleration
(d) zero acceleration

Satpal Satpal
Satpal Satpal
Numerade Educator
01:40

Problem 59

A particle accelerates from rest at a constant rate for some time moving along a straight line and attains a velocity of $8 \mathrm{~m} \mathrm{~s}^{-1} .$ Immediately it decelerates at a constant rate and comes to rest. If the total time taken is $4 \mathrm{~s}$, the distance travelled is
(a) $32 \mathrm{~m}$
(b) $16 \mathrm{~m}$
(c) $4 \mathrm{~m}$
(d) $2 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:20

Problem 60

A body moves along a straight line with constant acceleration for $20 \mathrm{~s}$ after it starts from rest. It covers a distance $\mathrm{S}$ in the first 10 seconds and $\mathrm{S}$, in the next 10 seconds of its motion. Relation between $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ is
(a) $\mathrm{S}_{2}=3 \mathrm{~S}_{1}$
(b) $\mathrm{S}_{2}=4 \mathrm{~S}_{1}$
(c) $\mathrm{S}_{2}=2 \mathrm{~S}_{1}$
(d) $\mathrm{S}_{2}=\mathrm{S}_{1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:40

Problem 61

A particle moves along X-axis in such a way that its $x$ -coordinate varies with time $t$ according to the relation $x=2-5 t$ $+6 \mathrm{t}^{2}$. The initial velocity $($ at $\mathrm{t}=0)$ of the particle is
(a) $-5$ unit
(b) 3 unit
(c) 6 unit
(d) $-6$ unit

Satpal Satpal
Satpal Satpal
Numerade Educator
02:45

Problem 62

The motors of an electric train can give it a uniform acceleration of $1 \mathrm{~m} \mathrm{~s}^{-2}$ and the brakes can give it a uniform negative acceleration of $3 \mathrm{~m} \mathrm{~s}^{-2}$. The shortest time in which the train can make a trip, starting from a station and stopping at another station that is separated from the starting station by a distance of $1350 \mathrm{~m}$ on straight track, is
(a) $15 \mathrm{~s}$
(b) $30 \mathrm{~s}$
(c) $60 \mathrm{~s}$
(d) $120 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:16

Problem 63

An electron starting from rest and moving along a straight line has a velocity that increases linearly with time, i.e., $\mathrm{v}=\mathrm{kt}$ where $\mathrm{k}=2 \mathrm{~m} \mathrm{~s}^{-2}$. The distance covered by the electron in the first 3 second will be
(a) $9 \mathrm{~m}$
(b) $16 \mathrm{~m}$
(c) $27 \mathrm{~m}$
(d) $36 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:04

Problem 64

The displacement of a particle moving along a straight line at time ' $\mathrm{t}$ ' is given by $\mathrm{x}=1+2 \mathrm{t}+3 \mathrm{t}^{2}$. The instantaneous acceleration is
(a) Zero
(b) 6 unit
(c) $(2+6 \mathrm{t})$ unit
(d) $6 \mathrm{t}$ unit

Satpal Satpal
Satpal Satpal
Numerade Educator
01:33

Problem 65

From the top of a tower of height $20 \mathrm{~m}$, a boy drops one stone; one second later he throws another stone vertically downwards so that both hit the ground together. The initial velocity of the second stone is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $10 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $15 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $20 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $25 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:09

Problem 66

A body released from the top of a tower of height 'h' takes 't' second to reach the ground. At time $\frac{1}{2} \mathrm{t}$ the height of the body from the ground is
(a) $\frac{\mathrm{h}}{4}$
(b) $\frac{\mathrm{h}}{3}$
(c) $\frac{\mathrm{h}}{2}$
(d) $\frac{3 \mathrm{~h}}{4}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:11

Problem 67

A body dropped from a tower travels half of the total distance in the last second of its motion. The total time of fall will be $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $\sqrt{2} \mathrm{~s}$
(b) $2 \mathrm{~s}$
(c) $2+\sqrt{2} \mathrm{~s}$
(d) $2 \sqrt{2} \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:18

Problem 68

Two bodies are thrown vertically upwards, with their initial velocities in the ratio $2: 3$. The ratio of maximum heights attained will be
(a) $\sqrt{2}: \sqrt{3}$
(b) $4: 9$
(c) $2: 3$
(d) Data is insufficient

Satpal Satpal
Satpal Satpal
Numerade Educator
02:00

Problem 69

A balloon is at a height of $12.8 \mathrm{~m}$ above the ground and is ascending with a velocity of $12 \mathrm{~m} \mathrm{~s}^{-1} .$ A $2 \mathrm{~kg}$ body is dropped from it. It will reach the ground in $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $1.5 \mathrm{~s}$
(b) $2 \mathrm{~s}$
(c) $3.2 \mathrm{~s}$
(d) $4.5 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:24

Problem 70

A body starts from rest and falls through a height of $19.6 \mathrm{~m}$. The time it takes to fall through the last $4.9 \mathrm{~m}$ of its fall is
(a) $0.4 \mathrm{~s}$
(b) $0.268 \mathrm{~s}$
(c) $0.05 \mathrm{~s}$
(d) $0.1 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:22

Problem 71

Two bodies of masses $m_{1}$ and $m_{2}$ are dropped from rest from heights $h_{1}$ and $h_{2} .$ The ratio of their respective time to reach the ground is
(a) $\sqrt{\mathrm{m}_{1}} \mathrm{~h}_{1}: \sqrt{\mathrm{m}_{2}} \mathrm{~h}_{2}$
(b) $\mathrm{h}_{1}: \mathrm{h}_{2}$
(c) $\mathrm{m}_{1} \sqrt{\mathrm{h}_{1}}: \mathrm{m}_{2} \sqrt{\mathrm{h}_{2}}$
(d) $\sqrt{h_{1}}: \sqrt{h_{2}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:58

Problem 72

A body is released from a certain height. Another one is released from the same height a second later. The separation between the bodies 2 s after the release of the second body is
(a) $24.5 \mathrm{~m}$
(b) $4.9 \mathrm{~m}$
(c) $9.8 \mathrm{~m}$
(d) $14.7 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:37

Problem 73

A stone thrown vertically upwards with a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{1}$. Another stone thrown vertically upwards from the same point with a velocity $10 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{2}$. The relation between $\mathrm{h}_{1}$ and $\mathrm{h}_{2}$ is
(a) $\mathrm{h}_{1}=\mathrm{h}_{2} / 2$
(b) $\mathrm{h}_{2}=2 \mathrm{~h}_{1}$
(c) $\mathrm{h}_{1}=3 \mathrm{~h}_{2}$
(d) $\mathrm{h}_{2}=4 \mathrm{~h}_{1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:44

Problem 74

The distance travelled by a body falling freely from rest in first, second and third second of its fall are in the ratio
(a) $1: 2: 3$
(b) $1: 3: 5$
(c) $1: 4: 9$
(d) $1: 5: 11$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:30

Problem 75

When a body is thrown up, at the highest point, its velocity is zero. Its acceleration is (upward positive)
(a) Zero
(b) $\mathrm{g}$
(c) $\mathrm{g} / 2$
(d) -g

Satpal Satpal
Satpal Satpal
Numerade Educator
02:20

Problem 76

A man stands on the edge of a cliff at a height above the ground. He throws a ball A straight up with an initial speed u and another ball B straight down with the same initial speed. When the balls hit the ground,
(a) speed of ball $\mathrm{A}=$ speed of ball $\mathrm{B}$
(b) speed of ball $\mathrm{A}>$ speed of ball $\mathrm{B}$
(c) speed of ball $\mathrm{B}>$ speed of ball $\mathrm{A}$
(d) speed of ball $\mathrm{A} \geq$ speed of ball $\mathrm{B}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:38

Problem 77

A train of length $200 \mathrm{~m}$ travelling at $30 \mathrm{~m} \mathrm{~s}^{-1}$ overtakes another train of length $300 \mathrm{~m}$ travelling at $20 \mathrm{~m} \mathrm{~s}^{-1}$ in the same direction on a parallel track. The time taken by the first train to cross the second is
(a) $30 \mathrm{~s}$
(b) $50 \mathrm{~s}$
(c) $10 \mathrm{~s}$
(d) $20 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:04

Problem 78

A wooden block is dropped from the top of a building $100 \mathrm{~m}$ high above ground. Simultaneously a bullet is fired from the foot of the building upwards with a velocity of $100 \mathrm{~m} \mathrm{~s}^{-1}$. The height above the ground at which they meet is
(a) $90.2 \mathrm{~m}$
(b) $4.9 \mathrm{~m}$
(c) $95.1 \mathrm{~m}$
(d) $9.8 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:00

Problem 79

A stone is projected vertically upwards with a speed $\sqrt{2 \mathrm{gh}}$. At the same time another stone is dropped downwards from a point in the same vertical line located at a height h above the ground. The height of the point above the ground where the two bodies collide is
(a) $\frac{2 \mathrm{~h}}{3}$
(b) $\frac{\mathrm{h}}{2}$
(c) $\frac{3 \mathrm{~h}}{4}$
(d) $\frac{\mathrm{h}}{4}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:58

Problem 80

Time taken by a boat to travel a distance $2 \mathrm{~d}$ in still water is $\mathrm{t}_{\mathrm{stil} \|}$. The same boat travels in flowing river; going downstream for a distance of $\mathrm{d}$ and returning to the starting point, taking a total time of $\mathrm{t}_{\text {flow }}$. The correct relationship is
(a) $\mathrm{t}_{\text {still }}=\mathrm{t}_{\text {flow }}$
(b) $\mathrm{t}_{\text {flow }}<\mathrm{t}_{\text {still }}$
(c) $\mathrm{t}_{\text {still }}<\mathrm{t}_{\text {flow }}$
(d) $\mathrm{t}_{\text {still }}=2 \mathrm{t}_{\text {flow }}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:08

Problem 81

The velocity-time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in $8 \mathrm{~s}$ are
(a) $12 \mathrm{~m}, 20 \mathrm{~m}$
(b) $14 \mathrm{~m}, 12 \mathrm{~m}$
(c) $16 \mathrm{~m}, 20 \mathrm{~m}$
(d) $12 \mathrm{~m}, 16 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:18

Problem 82

An swimmer completes one round (A to $B$ and back) of a pool of length $50 \mathrm{~m}$ in 80 second. The displacement of the swimmer at the end of 5 minute and 12 second is
(a) $10 \mathrm{~m}$
(b) $50 \mathrm{~m}$
(c) $40 \mathrm{~m}$
(d) $30 \mathrm{~m}$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:57

Problem 83

The greatest acceleration or deceleration that a train may have is a. The minimum time in which the train can start from one station to stop at the next (at a straight distance of $s)$ is
(a) $\sqrt{\frac{\mathrm{s}}{\mathrm{a}}}$
(b) $\sqrt{\frac{2 \mathrm{~s}}{\mathrm{a}}}$
(c) $\frac{1}{2} \sqrt{\frac{s}{a}}$
(d) $2 \sqrt{\frac{\mathrm{s}}{\mathrm{a}}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:14

Problem 84

A bullet fired into a large block of wood of uniform resistance, hits the block with a velocity of $48 \mathrm{~m} \mathrm{~s}^{-1}$. It penetrates a distance of $60 \mathrm{~cm}$ and the velocity is then reduced to $24 \mathrm{~m} \mathrm{~s}^{-1}$. It then penetrates a further distance of (in $\mathrm{cm}$ )
(a) 50
(b) 16
(c) 18
(d) 20

Satpal Satpal
Satpal Satpal
Numerade Educator
02:06

Problem 85

A uniformly accelerating train passes a person on the ground. If the speeds of the points 1,2 and 3 on the train as they pass the person are $\mathrm{u}_{1}, \mathrm{u}_{2}$ and $\mathrm{u}_{3}$ respectively and $\frac{\mathrm{u}_{1}}{\mathrm{u}_{2}}=\frac{\mathrm{u}_{2}}{\mathrm{u}_{3}}$, then $\frac{\mathrm{s}_{1}}{\mathrm{~s}_{2}}$ is (where, $\mathrm{s}_{1}$ is the distance between 1 and $2 ; s_{2}$ between 2 and 3 respectively),
(a) $\frac{s_{1}}{s_{2}}=\frac{u_{2}}{u_{3}}$
(b) $\frac{s_{1}}{s_{2}}=\left(\frac{u_{1}}{u_{2}}\right)^{2}$
(c) $\frac{s_{1}}{s_{2}}=\frac{u_{3}}{u_{1}}$
(d) $\frac{s_{1}}{s_{2}}=\frac{u_{3}-u_{2}}{u_{2}-u_{1}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:12

Problem 86

A car travels in a straight line with varying velocity given by $\mathrm{v}=\left|\mathrm{t}-\mathrm{t}_{0}\right| \mathrm{m} \mathrm{s}^{-1}$ for $0 \leq \mathrm{t} \leq 2 \mathrm{t}_{0}$ where, $\mathrm{t}=$ time and $\mathrm{t}_{0}=$ time at which velocity is zero. The distance travelled by the car in this interval is
(a) $\mathrm{t}_{0}^{2}$
(b) $2 \mathrm{t}_{0}^{2}$
(c) $\frac{3}{2} t_{0}^{2}$
(d) 0

Satpal Satpal
Satpal Satpal
Numerade Educator
02:25

Problem 87

Two bodies move with uniform acceleration along a straight line. The ratio of the initial speeds of the bodies is $2: 1$ and the ratio of their accelerations is $1: 2$ respectively. Then the ratio of the instantaneous speeds of the bodies at any time $\mathrm{t}$ is
(a) $1: 1$
(b) $1: 4$
(c) $2: 1$
(d) Ratio varies with time

Satpal Satpal
Satpal Satpal
Numerade Educator
02:31

Problem 88

A long, straight rope lying on a floor is pulled along its length with uniform acceleration along its length. If the velocities of the front and back ends of the rope when it passes through a particular point on the floor are $2 \mathrm{~m} \mathrm{~s}^{-1}$ and $4 \mathrm{~m}$ $\mathrm{s}^{-1}$ respectively, the velocity of the midpoint of the rope when it passes through the same point is (in $\left.\mathrm{m} \mathrm{s}^{-1}\right)$
(a) $2 \sqrt{2}$
(b) $\sqrt{10}$
(c) 3
(d) $2.67$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:51

Problem 89

A point object starts from rest from the origin and moves with a uniform acceleration (in $\left.\mathrm{m} \mathrm{s}^{-2}\right)$ of $\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}$. The distance of the object from the origin after 1 second is
(a) $\frac{\sqrt{\alpha^{2}+\beta^{2}+\gamma^{2}}}{2}$
(b) $\frac{\sqrt{\alpha \beta+\beta \gamma+\gamma \alpha}}{2}$
(c) $(\alpha+\beta+\gamma)$
(d) $\quad(\alpha+\beta+\gamma)^{2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:09

Problem 90

A particle moving along a straight line with uniform acceleration covers distances $\mathrm{AB}=8 \mathrm{~m}$ and $\mathrm{BC}=18 \mathrm{~m}$ in one second each. The speed of the particle at point $\mathrm{B}$ is (in $\left.\mathrm{m} \mathrm{s}^{-1}\right)$
(a) 13
(b) 8
(c) 5
(d) 10

Satpal Satpal
Satpal Satpal
Numerade Educator
02:14

Problem 91

Three points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are on a straight line such that $\mathrm{AB}=\mathrm{BC}$. A particle moving with uniform acceleration passes A and $C$ with speeds of $6 \mathrm{~m} \mathrm{~s}^{-1}$ and $8 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. Aother particle moving with uniform acceleration passes $\mathrm{A}$ and $\mathrm{B}$ with speeds of $12 \mathrm{~m} \mathrm{~s}^{-1}$ and $14 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. If $\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ are the times taken by the particles to cross $\mathrm{AB}, \frac{\mathrm{t}_{1}}{\mathrm{t}_{2}}$ is nearly
(a) $2.0$
(b) $1.3$
(c) $\sqrt{2}$
(d) $0.5$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:25

Problem 92

A stone falls into a well. If it hits the water in $3 \mathrm{~s}$ from its release, the depth to water surface from the mouth of the well is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $100 \mathrm{~m}$
(b) $50 \mathrm{~m}$
(c) $30 \mathrm{~m}$
(d) $45 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:27

Problem 93

A balloon with a basket, with a man inside, starts from rest and rises vertically with a uniform acceleration of $4.9 \mathrm{~m}$ $\mathrm{s}^{-2} .$ The man releases a ball 2 second after the balloon leaves the ground. The maximum height above the ground attained by the ball is
(a) $9.8 \mathrm{~m}$
(b) $14.7 \mathrm{~m}$
(c) $19.6 \mathrm{~m}$
(d) $24.5 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:40

Problem 94

If an object falling vertically from rest takes $\Delta$ t second less and acquires a velocity of $\mathrm{u} \mathrm{m} \mathrm{s}^{-1}$ more in falling through the same distances on 2 planets having accelerations due to gravity of $2 \mathrm{~g}$ and $8 \mathrm{~g}$ respectively, then
(a) $\mathrm{u}=4 \mathrm{~g} \Delta \mathrm{t}$
(b) $\mathrm{u}=2 \mathrm{~g} \Delta \mathrm{t}$
(c) $\mathrm{u}=10 \mathrm{~g} \Delta \mathrm{t}$
(d) $\mathrm{u}=2 \sqrt{2} \mathrm{~g} \Delta \mathrm{t}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:32

Problem 95

If air resistance is to be considered while analysing the motion of a particle thrown vertically upwards, which of the following relationships between time of ascent $\left(\mathrm{t}_{\mathrm{asc}}\right)$ and time of descent $\left(\mathrm{t}_{\mathrm{des}}\right)$ is correct?
(a) $\mathrm{t}_{\text {asc }}=\mathrm{t}_{\text {dess }}$
(b) $\mathrm{t}_{\mathrm{asc}}>\mathrm{t}_{\mathrm{des}}$
(c) $\mathrm{t}_{\text {asc }}<\mathrm{t}_{\text {des }}$
(d) Either b or c depending on the mass of the projectile.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:40

Problem 96

A particle is thrown vertically upwards with a speed of $50 \mathrm{~m} \mathrm{~s}^{-1}$. The ratio of the distance travelled in the 5 th second to that in the 6 th second is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $2: 1$
(b) $5: 3$
(c) $4: 5$
(d) $1: 1$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:46

Problem 97

A boy P stands on top of a tower. Another boy Q throws a ball vertically up from the ground so that it just reaches $\mathrm{P}$ and the time taken is $\mathrm{t}_{0}$. The speed with which P should throw the ball vertically downwards so that it reaches the ground in time $\frac{\mathrm{t}_{0}}{2} \mathrm{i}$
(a) $\mathrm{gt}_{0}$
(b) $2 \mathrm{gt}_{0}$
(c) $\frac{3}{4} \mathrm{gt}_{0}$
(d) $\frac{\mathrm{gt}_{0}}{4}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:23

Problem 98

A man throws balls into the air one after another. He always throws a ball when the previous one thrown has just reached the highest point. The height to which each ball rises, if he throws 5 balls per second is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $0.31 \mathrm{~m}$
(b) $0.20 \mathrm{~m}$
(c) $0.42 \mathrm{~m}$
(d) $0.53 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:00

Problem 99

Two stones are dropped from the top of a tower at half a second apart. The time after dropping the first stone at which the distance between the two stones is $20 \mathrm{~m}$ is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $4 \mathrm{~s}$
(b) $3.75 \mathrm{~s}$
(c) $4.25 \mathrm{~s}$
(d) $2 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:19

Problem 100

In a circus, a juggler throws balls vertically upwards at intervals of $2 \mathrm{~s}$. He throws a ball when the previous one is at the highest point. Then the maximum height to which each ball rises is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $20 \mathrm{~m}$
(b) $45 \mathrm{~m}$
(c) $25 \mathrm{~m}$
(d) $15 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:30

Problem 101

The speed with which a stone dropped from a cliff $160 \mathrm{~m}$ high, hits the sea below is nearly $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $150 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $56 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $60 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $59 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:20

Problem 102

Two bodies are thrown vertically upwards from walls of heights $2.2 \mathrm{~m}$ and $1.05 \mathrm{~m}$ respectively, with an initial velocity of $10 \mathrm{~m} \mathrm{~s}^{-1}$. The ratio of their times of flight is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $\frac{22}{21}$
(b) $\frac{12}{11}$
(c) $\frac{44}{23}$
(d) $\frac{13}{11}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:20

Problem 102

Body A begins to move with an initial velocity of $2 \mathrm{~m} \mathrm{~s}^{-1}$ and a constant acceleration a. $10 \mathrm{~s}$ later, body $\mathrm{B}$ starts from the same point with an initial velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ in the same direction as 'A' and with the same constant acceleration $\mathrm{a}$.
(i) What is the maximum value of 'a for which body B will overtake A?
(ii) If overtaking takes place at $\mathrm{t}=25 \mathrm{~s}$, what is a?

Satpal Satpal
Satpal Satpal
Numerade Educator
01:52

Problem 103

A body is thrown vertically up with a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$ from the top of a wall of height $3.45 \mathrm{~m}$. The height from which another body should be dropped simultaneously such that the two bodies reach the ground at the same time is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $40 \mathrm{~m}$
(b) $24.5 \mathrm{~m}$
(c) $6.9 \mathrm{~m}$
(d) $20 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:13

Problem 104

Three construction workers can throw bricks vertically up with speeds of $4 \mathrm{~m} \mathrm{~s}^{-1}, 6 \mathrm{~m} \mathrm{~s}^{-1}$ and $12 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. Working together, they can stack them on a platform of maximum height (in $\mathrm{m}$ )
(a) 5
(b) 10
(c) 15
(d) 20

Satpal Satpal
Satpal Satpal
Numerade Educator
01:43

Problem 105

A body is thrown vertically up with a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$ from a tower of height $15 \mathrm{~m}$. The magnitude of its average velocity for the journey is (in $\mathrm{m} \mathrm{s}^{-1}$ )
(a) 5
(b) 10
(c) 15
(d) 20

Satpal Satpal
Satpal Satpal
Numerade Educator
02:14

Problem 106

A man is standing on a platform behind a wall of height $11.25 \mathrm{~m}$ as shown. The platform he is standing on is at a height of $8.75 \mathrm{~m}$. The minimum time (in $\mathrm{s}$ ) in which a person on the ground on the other side of the wall can throw him a tool is $\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:56

Problem 107

An elevator car whose floor to ceiling distance is equal to $2.7 \mathrm{~m}$, starts from rest and ascends with a constant acceleration of $1.2 \mathrm{~m} \mathrm{~s}^{-2} .$ Two seconds later, a bolt drops from the car's ceiling. The time taken by the bolt to hit the floor of the elevator is
(a) $1 \mathrm{~s}$
(b) $0.8 \mathrm{~s}$
(c) $1.2 \mathrm{~s}$
(d) $0.7 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:24

Problem 108

The positions of three particles are as follows:
(i) $x=3 t+2.5 t^{2}$
(ii) $\mathrm{x}=\frac{5}{2} \mathrm{t}(2+\mathrm{t})$
(iii) $x=6+3 t-2.5 t^{2}$
Relative motion is uniform between
(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iii)
(d) both (i) and (ii) and (i) and (iii)

Satpal Satpal
Satpal Satpal
Numerade Educator
01:25

Problem 109

Inside a lift, which is moving vertically upwards with a uniform acceleration a', a body is projected vertically upwards with a speed 'u' with respect to the lift. Its time of flight inside the lift is
(a) $\frac{2 \mathrm{u}}{\mathrm{a}+\mathrm{g}}$
(b) $\frac{2 \mathrm{u}}{\mathrm{a}-\mathrm{g}}$
(c) $\frac{2 \mathrm{u}}{\mathrm{g}}$
(d) $\frac{2 \mathrm{u}}{\mathrm{a}}$
110. An elevator is going down with a constant acceleration. A coin dropped from a point $1.8 \mathrm{~m}$ above the elevator floor takes one second to reach the floor. The magnitude of the acceleration of the elevator (in $\mathrm{m} \mathrm{s}^{-2}$ ) is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $3.6$
(b) 5
(c) $7.2$
(d) $6.4$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:28

Problem 110

An elevator is going down with a constant acceleration. A coin dropped from a point $1.8 \mathrm{~m}$ above the elevator floor takes one second to reach the floor. The magnitude of the acceleration of the elevator (in $\mathrm{m} \mathrm{s}^{-2}$ ) is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $3.6$
(b) 5
(c) $7.2$
(d) $6.4$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:57

Problem 111

Statement 1 A bus starting from rest, moves on a straight road and away from a person at some distance behind the bus, with an acceleration along the straight road given by the expression $\mathrm{a}=\mathrm{kt}^{3}$ ( where $\mathrm{k}=$ a constant and $\mathrm{t}=$ time $)$. When the person travels on the straight road with the minimum constant speed required for catching the bus, the speeds of the bus and man are the same at the instant he catches the bus.
and
Statement 2 For the minimum possible speed, the displacement time plot of the person is tangent to that of the bus.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:50

Problem 112

Statement 1 For a body thrown vertically up from the ground, the distance covered in the first second is equal to the distance covered in the last second only if the initial velocity is greater than $10 \mathrm{~m} \mathrm{~s}^{-1}\left(\mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$.
and
Statement 2 For the upward and downward journeys to take more than one second, the initial speed has to be greater than $10 \mathrm{~m} \mathrm{~s}^{-1}$.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:58

Problem 113

Statement 1 Two particles $\mathrm{A}$ and $\mathrm{B}$ are projected vertically upwards from the top of two identical towers, one on Earth and the other on Moon, with the same initial speed. The magnitudes of the displacement of $\mathrm{A}$ and $\mathrm{B}$ in the first second of projection can be the same.
and
Statement 2 The acceleration due to gravity on the surface of Earth is 6 times that on the surface of Moon.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:08

Problem 114

The velocity of the particle at time $\mathrm{t}=4 \mathrm{~s}$ is (in $\left.\mathrm{m} \mathrm{s}^{-1}\right)$
(a) 4
(b) 8
(c) 6
(d) 7

Satpal Satpal
Satpal Satpal
Numerade Educator
01:39

Problem 115

The displacement of the particle during the interval $\mathrm{t}=2 \mathrm{~s}$ to $\mathrm{t}=8 \mathrm{~s}$ is
(a) $54 \mathrm{~m}$
(b) $12 \mathrm{~m}$
(c) $24 \mathrm{~m}$
(d) $48 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:28

Problem 116

The maximum velocity attained by the particle is
(a) $24 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $25 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $26 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $30 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:39

Problem 117

A bullet plunges vertically into a retarding medium with an initial velocity u. Its velocity is reduced by $20 \%$ in a distance of $0.9 \mathrm{~m}$ in the medium. If a is the uniform retardation in the medium, then:
(a) The total distance travelled by the bullet in the medium is $2.5 \mathrm{~m}$.
(b) The total distance travelled by the bullet in the medium is $1.6 \mathrm{~m}$.
(c) Its average velocity in the medium is numerically equal to $\frac{\sqrt{5 a}}{2}$.
(d) The time of travel in the medium is numerically equal to $\sqrt{\frac{5}{\text { a }}}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:57

Problem 118

A body $\mathrm{A}$ is given an initial velocity $\mathrm{v}$ in the $\mathrm{X}$ -direction at $\mathrm{t}=0$; its velocity is increased by $\mathrm{v}$ in the same direction at the end of every second. Another body B starting from zero velocity is given a uniform acceleration 'a' in X-direction. Both travel the same distance for $\mathrm{n}$ second.
(a) Acceleration $\mathrm{a}=\mathrm{v}\left(1+\frac{1}{\mathrm{n}}\right)$.
(b) The distance travelled by the first body in $20 \mathrm{~s}$ is $210 \mathrm{v}$ metre.
(c) If $\mathrm{n}$ is large, in 5 th second both travel the same distance.
(d) If $n$ is large, for even values of $n$, in the $\left(\frac{n}{2}\right)$ second both travel equal distance; if $n$ is odd, at $\frac{n+1}{2}$ second they travel equal distance.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:17

Problem 119

A body projected vertically upward with a velocity $\mathrm{v}$ at $\mathrm{t}=0$ is found at a height $\mathrm{h}$ after 1 second and after a further 6 second, it is found at the same height $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$. Then
(a) $\mathrm{h}$ is $30 \mathrm{~m}$
(b) $\mathrm{u}$ is $40 \mathrm{~m} \mathrm{~s}^{-1}$
(c) maximum height is $80 \mathrm{~m}$.
(d) distance moved in 5 th second is $5 \mathrm{~m}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:13

Problem 120

Column I
(a) The position time graph of a body in $1 \mathrm{D}$ motion with constant acceleration (positive, negative or zero).
(b) The position-time graph of a body in1D motion with constant velocity.
(c) The position time graph of a body dropped from a height $\mathrm{H}$ rebounding to the same height.
(d) The velocity time graph of a body in $1 \mathrm{D}$ motion with constant acceleration.
Column II
(p) Graph cannot copy
(q)Graph cannot copy
(r)Graph cannot copy
(s)Graph cannot copy

Ajay Singhal
Ajay Singhal
Numerade Educator
01:33

Problem 121

A block released from rest on an inclined plane slides down as shown. The motion of the block with respect to the given system is
(a) one dimensional.
(b) two dimensional.
(c) three dimensional.
(d) one and two dimensional.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:10

Problem 122

The above graph can represent
(a) distance vs $t$
(b) displacement vs t
(c) (a) or (b)
(d) neither (a) nor (b)

Satpal Satpal
Satpal Satpal
Numerade Educator
02:13

Problem 123

The graph shown was obtained for a body undergoing uniformly accelerated motion along a straight line. The plot could be (y and x-axes respectively)
(a) time vs displacement
(b) velocity vs displacement
(c) time vs speed
(d) (a) or (b)

Satpal Satpal
Satpal Satpal
Numerade Educator
02:13

Problem 124

A ball is released from a height above a floor and comes to rest after a few bounces. The displacement time graph of the motion is given by
(a)
(b)
(c)
(d)

Satpal Satpal
Satpal Satpal
Numerade Educator
01:52

Problem 125

A ball is bouncing back and forth with constant speed between two walls. The velocity vs displacement graph of the motion is given by
(a)
(b)
(c)
(d)

Satpal Satpal
Satpal Satpal
Numerade Educator
03:24

Problem 126

Two bodies $\mathrm{A}$ and $\mathrm{B}$, initially at the origin and moving along the same straight line have velocities as shown. If the total distance covered by $\mathrm{A}$ and $\mathrm{B}$ in time $\mathrm{t}_{2}$ is the same, then
(a) $\mathrm{t}_{1}=\frac{\mathrm{t}_{2}}{2}$
(b) $\mathrm{B}$ overtakes $\mathrm{A}$ at $\mathrm{t}=\mathrm{t}_{1}$
(c) average velocity of $\mathrm{A}>$ average velocity of $\mathrm{B}$
(d) both (a) and (b) are true

Satpal Satpal
Satpal Satpal
Numerade Educator
01:58

Problem 127

A particle starting from rest and moving along a straight line has acceleration a for time $\mathrm{t}_{1}$ and acceleration-a for time $\mathrm{t}_{2}$. If the total displacement of the body is zero, then $\frac{\mathrm{t}_{2}}{\mathrm{t}_{1}}$ is
(a) 1
(b) 2
(c) $\sqrt{2}$
(d) $\sqrt{2}+1$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:32

Problem 128

The velocity time graph of a particle starting from the origin at time $\mathrm{t}=0$ and moving along a straight line is as shown. If $\mathrm{A}_{1}, \mathrm{~A}_{2}$ and $\mathrm{A}_{3}$ are the shaded areas and $\mathrm{A}_{2}>2 \mathrm{~A}_{1}$ and $\mathrm{A}_{3}<\mathrm{A}_{1}$, the number of times the particle crosses the origin is
(a) 0
(b) 1
(c) 2
(d) 3

Ajay Singhal
Ajay Singhal
Numerade Educator
01:52

Problem 129

A sports car is moving on a straight road at a speed of 288 kmph. The air brakes are applied till the speed reaches $144 \mathrm{kmph}$, producing a uniform deceleration of $10 \mathrm{~m} \mathrm{~s}^{-2}$. At $144 \mathrm{~km}$ ph speed, the regular brakes are applied till the car stopped, producing a uniform deceleration of $5 \mathrm{~m} \mathrm{~s}^{-2} .$ The distance travelled by the car, from the instant of applying the air brakes till it stopped, is (in $\mathrm{m}$ )
(a) 320
(b) 400
(c) 512
(d) 640

Satpal Satpal
Satpal Satpal
Numerade Educator
02:15

Problem 130

A particle starts from rest and travels a total distance of $18 \mathrm{~m}$ along a straight path. The first half of the distance was travelled with a uniform acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ and the rest with uniform velocity. The average velocity for the whole journey is (in $\mathrm{m} \mathrm{s}^{-1}$ )
(a) 3
(b) 4
(c) 6
(d) 9

Satpal Satpal
Satpal Satpal
Numerade Educator
02:46

Problem 131

A particle starts from rest and travels a straight distance of $18 \mathrm{~m}$. The first half of the distance is covered with a uniform acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ while the second half is covered with a uniform acceleration of $2.5 \mathrm{~m} \mathrm{~s}^{-2}$. The total time taken for the journey is
(a) $4.2 \mathrm{~s}$
(b) $3.6 \mathrm{~s}$
(c) $5 \mathrm{~s}$
(d) $3 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:46

Problem 132

Train A can move with a uniform acceleration of $3 \mathrm{~m} \mathrm{~s}^{-2}$ while speeding up and with a uniform deceleration of $5 \mathrm{~m}$ $\mathrm{s}^{-2}$ on applying the brakes. Train $\mathrm{B}$ can move with a uniform acceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ while speeding up and with a uniform deceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ on applying the brakes. If $\mathrm{t}_{\mathrm{A}}$ and $\mathrm{t}_{\mathrm{B}}$ are the minimum times taken by train $\mathrm{A}$ and train $B$ respectively to start from one station and stop at the next station while travelling on straight tracks, then
(a) $\mathrm{t}_{\mathrm{A}}=\mathrm{t}_{\mathrm{B}}$
(b) $\mathrm{t}_{\mathrm{A}}>\mathrm{t}_{\mathrm{B}}$
(c) $\mathrm{t}_{\mathrm{A}}<\mathrm{t}_{\mathrm{B}}$
(d) $\frac{\mathrm{t}_{\mathrm{A}}}{\mathrm{t}_{\mathrm{B}}}$ depends on the distance between stations.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:05

Problem 133

The velocity time graph of a body in one dimensional motion is as shown. The number of times the average acceleration is equal to the instantaneous acceleration during the motion is
(a) 0
(b) 1
(c) 2
(d) 3

Satpal Satpal
Satpal Satpal
Numerade Educator
02:13

Problem 134

The displacement time graph of two bodies $\mathrm{A}$ and $\mathrm{B}$ in $1 \mathrm{D}$ motion in the same direction is as shown
(a) their relative velocity is zero at a time $t<t_{1}$
(b) their relative velocity is zero at a time $t_{1}<t<t_{2}$
(c) the distance between the bodies is maximum at $\mathrm{t}=\mathrm{t}_{1}$
(d) the relative acceleration is zero at some point

Satpal Satpal
Satpal Satpal
Numerade Educator
01:40

Problem 135

A body starts with a certain initial velocity and moves with a constant deceleration along a straight line. If the distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the body will come to a stop in time
(a) $40 \mathrm{~s}$
(b) $30 \mathrm{~s}$
(c) $20 \mathrm{~s}$
(d) $10 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:24

Problem 136

A body starts with a certain initial velocity and moves with constant deceleration along a straight line. If distances travelled in the 5 th and 7 th second are in the ratio $\frac{31}{27}$, the distance travelled by the body before it stops is
(a) $50 \mathrm{~m}$
(b) $100 \mathrm{~m}$
(c) $150 \mathrm{~m}$
(d) data insufficient

Satpal Satpal
Satpal Satpal
Numerade Educator
01:17

Problem 137

A body is dropped from a tower of height $45 \mathrm{~m}$. Another body is thrown up at the same instant with speed $\mathrm{u}$ from a height of $30 \mathrm{~m}$. If they reach the ground simultaneously, $\mathrm{u}$ is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $5 \mathrm{~ms}^{-1}$
(b) $10 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $15 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $20 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:04

Problem 138

A body dropped from a tower hits an obstacle $20 \mathrm{~m}$ below so that its speed is halved. If the total time of flight is $4 \mathrm{~s}$, the height of the tower (in $\mathrm{m}$ ) above the ground is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) 20
(b) 40
(c) 60
(d) 80

Satpal Satpal
Satpal Satpal
Numerade Educator
03:06

Problem 139

A paratrooper jumps from a height $\mathrm{H}$. The parachute can provide a uniform deceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$. The height above the ground at which the parachute should be opened so that he touches ground with zero speed is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $\frac{\mathrm{H}}{6}$
(b) $\frac{4 \mathrm{H}}{5}$
(c) $\frac{5 \mathrm{H}}{6}$
(d) $\frac{6 \mathrm{H}}{7}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:26

Problem 140

A body is projected vertically upwards with a speed of $12 \mathrm{~m} \mathrm{~s}^{-1}$ on the surface of a planet, where the acceleration due to its gravity is $8 \mathrm{~m} \mathrm{~s}^{-2}$. The time (in $\mathrm{s}$ ) for which it stays above a height of $5 \mathrm{~m}$ is
(a) 1
(b) 2
(c) 3
(d) 4

Satpal Satpal
Satpal Satpal
Numerade Educator
02:00

Problem 141

A body is thrown vertically up from a wall of height $2.2 \mathrm{~m}$ with a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$. The distance travelled in the last second of its motion is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $5 \mathrm{~m}$
(b) $6 \mathrm{~m}$
(c) $7 \mathrm{~m}$
(d) $8 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:19

Problem 142

A body dropped from a height of $20 \mathrm{~m}$ takes $1 \mathrm{~s}$ to cover a vertical pole on ground. If the body is dropped from a height of $40 \mathrm{~m}$, the time taken to cover the same pole is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $0.5 \mathrm{~s}$
(b) $\frac{1}{\sqrt{2}} \mathrm{~s}$
(c) $(2 \sqrt{2}-\sqrt{5})$ s
(d) $\frac{1}{\sqrt{3}} \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:56

Problem 143

A body A is dropped inside a pillar that is in the form of a tube and its inside has a constant downwa acceleration of $5 \mathrm{~m} \mathrm{~s}^{-2}$. The velocity with which another body $\mathrm{B}$ should be simultaneously throv up from the top of the pillar, so that it falls outside the tube and both bodies $\mathrm{A}$ and $\mathrm{B}$ reach ground at the same time, is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) $1.25 \mathrm{~m} \mathrm{~s}^{-1}$
(b) $2.5 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $5 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $7.5 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:33

Problem 144

Two bodies are projected vertically, from the mid point of a tower with equal speeds, so that one just reaches the top of the tower. The ratio of times of flight of the two bodies is
(a) 3
(b) 2
(c) $\sqrt{3}$
(d) $3+2 \sqrt{2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:31

Problem 145

A juggler throws balls up with equal speed. He releases a ball when the previous one has reached half the maximum height. The maximum number of balls moving in the upward direction at any one instant is
(a) 1
(b) 2
(c) 3
(d) 4

Satpal Satpal
Satpal Satpal
Numerade Educator
01:46

Problem 146

In the above problem, if the time in air of each ball is $2 \mathrm{~s}$, to have maximum number of balls in air, the reaction time should be about (ms)
(a) 50
(b) 100
(c) 240
(d) 400

Satpal Satpal
Satpal Satpal
Numerade Educator
02:34

Problem 147

A body is thrown from ground vertically upwards into an empty tank of height $\mathrm{H}$ in minimum time. The tank is now filled with water so that the acceleration inside is reduced to $\frac{\mathrm{g}}{2}$. The height h from which the body should be thrown so that the time is unchanged is
(a) $0.5 \mathrm{H}$
(b) $0.66 \mathrm{H}$
(c) $0.8 \mathrm{H}$
(d) $0.9 \mathrm{H}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:04

Problem 148

Three bodies are thrown vertically up simultaneously as shown in the figure, so that all three collide. Then
(a) $\mathrm{u}_{2}=\frac{\mathrm{u}_{1}+\mathrm{u}_{3}}{2}$
(b) $\mathrm{u}_{2}=\sqrt{\mathrm{u}_{1} \mathrm{u}_{3}}$
(c) $\mathrm{u}_{2}=\sqrt{\frac{\mathrm{u}_{1}^{2}+\mathrm{u}_{3}^{2}}{2}}$
(d) $\frac{2}{\mathrm{u}_{2}}=\frac{1}{\mathrm{u}_{1}}+\frac{1}{\mathrm{u}_{3}}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:23

Problem 149

Two bodies connected by a uniform flexible string have equation of motion along a straight line given by $x_{1}=3 t$ and $\mathrm{x}_{2}=6 \mathrm{t}+2 \mathrm{t}^{2}+10$ respectively, all ' $\mathrm{x}$ ' in metre and ' $\mathrm{t}$ ' in second. The time taken for the initial velocity of the mid-point of the string to double in magnitude is
(a) $2.25 \mathrm{~s}$
(b) $1.25 \mathrm{~s}$
(c) $2.5 \mathrm{~s}$
(d) $3.75 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:46

Problem 150

In a straight portion of a river, from a point $\mathrm{A}$ on the bank of the river as you move to a point $\mathrm{P}$ at a distance of $\mathrm{x}^{\prime} \mathrm{m}$ from A in the downstream direction, the speed of flow of river is equal to $2 \sqrt{9+0.1 x} \mathrm{~m} \mathrm{~s}^{-1} .$ A boat plies between $\mathrm{A}$ and another point B downstream. If the engine of the boat can produce a maximum speed of $36 \mathrm{kmph}$ on the boat in still water, the maximum range $\mathrm{AB}$ is (in $\mathrm{m}$ )
(a) 100
(b) 160
(c) 320
(d) 500

Satpal Satpal
Satpal Satpal
Numerade Educator
02:11

Problem 151

A body is thrown up, and another body is thrown down, from a tower of height h. The relative displacement vs time is given by
(a)
(b)
(c)
(d)

Satpal Satpal
Satpal Satpal
Numerade Educator
02:50

Problem 152

An aircraft carrier is designed to land aircraft of minimum speed $144 \mathrm{kmph}$. If the maximum speed of the carrier is $36 \mathrm{kmph}$, the minimum percentage increase in the length of the runway to just land aircraft of minimum speed $188 \mathrm{~km} \mathrm{~h}$ is (consider that the aircraft moves horizontally and in the same direction as the carrier, at the time of landing. The initial length of runway is designed for landing when the carrier is at rest).
(a) 5
(b) 10
(c) 18
(d) 20

Satpal Satpal
Satpal Satpal
Numerade Educator
01:36

Problem 153

A ball is dropped from a height 'h' above the ground. It loses $50 \%$ of its velocity on every impact with the ground before bouncing up. What is the total distance travelled by the ball when it finally comes to rest on the ground?
(a) $1.67 \mathrm{~h}$
(b) $2 \mathrm{~h}$
(c) $1.33 \mathrm{~h}$
(d) $2.5 \mathrm{~h}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:35

Problem 154

The uniform acceleration with which a man should start running from rest, behind a bus that goes past him with a constant speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ on a straight road, to catch it in $20 \mathrm{~m}$ distance from start, is
(a) $1 \mathrm{~m} \mathrm{~s}^{-2}$
(b) $2.5 \mathrm{~m} \mathrm{~s}^{-2}$
(c) $5 \mathrm{~m} \mathrm{~s}^{-2}$
(d) $10 \mathrm{~m} \mathrm{~s}^{-2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:28

Problem 155

Two cars with the same speed $v$ have constant decelerations of $a_{1}$ and $a_{2}\left(a_{1}<a_{2}\right)$ respectively at a point on the road. If they are travelling in the same direction on parallel roads, the difference in times in which they reach their destinations (where they stop moving), is
(a) $\mathrm{v}\left(\frac{1}{\mathrm{a}_{1}}-\frac{1}{\mathrm{a}_{2}}\right)$
(b) $\mathrm{v}\left(\frac{1}{\mathrm{a}_{1}}+\frac{1}{\mathrm{a}_{2}}\right)$
(c) $\frac{\mathrm{v}}{2}\left(\frac{1}{\mathrm{a}_{1}}-\frac{1}{\mathrm{a}_{2}}\right)$
(d) $\frac{1}{2}\left(\frac{v}{a_{1}-a_{2}}\right)$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:58

Problem 156

Two bodies are projected vertically upwards from a point with speeds of $20 \mathrm{~m} \mathrm{~s}^{-1}$ and $15 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. The second body rebounds from the ground with the same speed, and they meet in mid air. The relative velocity (in $\left.\mathrm{m} \mathrm{s}^{-1}\right)$ when they meet is $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) 15
(b) 25
(c) 35
(d) 45

Satpal Satpal
Satpal Satpal
Numerade Educator
02:12

Problem 157

A stone is dropped into a well. From the open mouth of the well, the water level is at a depth of $25 \mathrm{~m}$. The sound of splash is heard after $2.31$ s from its release. The speed of stone in air inside the well is (in $\mathrm{m} \mathrm{s}^{-1}$ ) (given $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
(a) 400
(b) 300
(c) 357
(d) 260

Satpal Satpal
Satpal Satpal
Numerade Educator
01:38

Problem 158

A man standing on a horizontal conveyor belt moving with a constant speed u, starts running with a constant acceleration a. The speed with which the man exits the conveyor belt after covering a length 'L' on it is
(a) $\sqrt{\mathrm{u}^{2}+2 \mathrm{aL}}$
(b) $\sqrt{\mathrm{u}^{2}+\mathrm{aL}}$
(c) $\sqrt{2 \mathrm{aL}}$
(d) u

Satpal Satpal
Satpal Satpal
Numerade Educator
03:38

Problem 159

Two bodies are projected vertically upwards with speeds $20 \mathrm{~m} \mathrm{~s}^{-1}$ and $15 \mathrm{~m} \mathrm{~s}^{-1}$ respectively from the same point. After the second body bounces once, they collide. If $\mathrm{t}_{1}$ and $\mathrm{t}_{2}$ are the time of flight of the second particle before bouncing
and time interval from bouncing till collision with first particle, then $\frac{t_{1}}{t_{2}}$ is
(a) 2
(b) 3
(c) 4
(d) 5

Satpal Satpal
Satpal Satpal
Numerade Educator
01:50

Problem 160

Two bodies separated by a distance of 's' start moving towards each other with speeds of $v$ and $2 v$ respectively. The uniform acceleration with which the first body should move so that they meet at the middle is
(a) $\frac{\mathrm{v}^{2}}{\mathrm{~s}}$
(b) $\frac{\mathrm{v}^{2}}{2 \mathrm{~s}}$
(c) $\frac{8 v^{2}}{s}$
(d) $\frac{4 v^{2}}{s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
04:10

Problem 161

Statement 1
If a body starting with velocity v, gets its velocity doubled at every equal intervals of distance, then its average velocity
for $\mathrm{n}$ equal intervals of distance is $\frac{\mathrm{nv}}{2}$, if $\mathrm{n}$ is very large,
and
Statement 2
Average velocity $=\frac{\text { Total displacement }}{\text { Total time }}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:59

Problem 162

Statement 1
For a body moving under constant acceleration, the total distance moved during a time duration, $\mathrm{t}$ has no bearing on the average velocity during that duration.
and
Statement 2
Displacement $\bar{s}=\bar{v}_{\text {avg }} \times t$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:39

Problem 163

Statement 1
Particle A is in uniform motion while particle B starts from rest and moves with uniform acceleration along a straight line. At an instant, the displacements of $\mathrm{A}\left(\mathrm{S}_{\mathrm{A}}\right)$ and $\mathrm{B}\left(\mathrm{S}_{\mathrm{B}}\right)$ are related as $\mathrm{S}_{\mathrm{A}}: \mathrm{S}_{\mathrm{B}}=2: 1$, and the magnitude of the velocities of $\mathrm{A}\left(\mathrm{V}_{\mathrm{A}}\right)$ and $\mathrm{B}\left(\mathrm{V}_{\mathrm{B}}\right)$ are equal at that instant.
and
Statement 2
$\mathrm{v}=$ at for uniformly accelerated motion of a body, starting from rest.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:48

Problem 164

Statement 1
If the average velocity and average acceleration of a particle in $1-\mathrm{D}$ motion is zero, during certain time interval, it need not be at rest in that duration.
and
Statement 2
The average values do not impose restrictions on the instantaneous values at every point.

Satpal Satpal
Satpal Satpal
Numerade Educator
03:11

Problem 165

Statement 1
A body thrown up will be having initial retardation and then acceleration under the influence of constant $\overline{\mathrm{g}}$.
and
Statement 2
Effective acceleration vector can be same for a body undergoing retardation or acceleration

Satpal Satpal
Satpal Satpal
Numerade Educator
02:17

Problem 166

Statement 1
Whatever may be the initial velocity of a vertical projectile, if its time of flight $\mathrm{T}$ is an odd integer, then its displacement
in $\left(\frac{\mathrm{T}+1}{2}\right)$ th second is zero.
and
Staement 2 For a body under uniform acceleration, displacement in nth second is $\overline{\mathrm{u}}+\frac{1}{2} \overline{\mathrm{a}}(2 \mathrm{n}-1)$.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:54

Problem 167

Statement 1 If the time of flight of a vertical projectile is an even integer $\mathrm{T}$, then its displacement in $\left(\frac{\mathrm{T}}{2}\right)^{\text {th }}$ second is numerically equal to $\frac{\mathrm{g}}{2}$.
and
Statement 2 The displacement in the nth second for a vertical projectile is $\bar{s}=\overline{\mathrm{u}}-\frac{1}{2} \overline{\mathrm{g}}(2 \mathrm{n}-1)$.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:27

Problem 168

Statement 1 When drops of water are falling down from a tap at regular intervals, at the instant when a drop just leaves the tap, the separations between adjacent drops are in arithmetic progression.
and
Statement 2
The distance travelled by the drop in the nth second is $\frac{1}{2} \mathrm{~g}(2 \mathrm{n}-1)$.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:42

Problem 169

Statement 1 When two bodies are projected vertically upward from a point on ground at different instants and with different velocities, if either of them is observed from the reference frame of the other body while both of them are in motion, then the observed body will be in linear motion with uniform velocity.
and
Statement 2
Their relative velocity is constant while they are in motion.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:55

Problem 170

Statement 1 When two particles travelling in a straight line in the same direction, have accelerations which are proportional to their velocity (same proportionality constant), there is only one speed for each particle at which the relative acceleration is unchanged.
and
Statement 2
In the above case, if the relative velocity is zero, relative acceleration is also zero.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:45

Problem 171

During the motion of the body, the acceleration maximum at
(a) $\mathrm{t}=0$ to $\mathrm{t}=2 \mathrm{~s}$
(b) $\mathrm{t}=2 \mathrm{~s}$ to $\mathrm{t}=4 \mathrm{~s}$
(c) $\mathrm{t}=4 \mathrm{~s}$ to $\mathrm{t}=6 \mathrm{~s}$
(d) $\mathrm{t}=8 \mathrm{~s}$ to $\mathrm{t}=10 \mathrm{~s}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:10

Problem 172

The average acceleration till time $\mathrm{t}=10 \mathrm{~s}$ is
(a) $2 \mathrm{~m} \mathrm{~s}^{-2}$
(b) $0.8 \mathrm{~m} \mathrm{~s}^{-2}$
(c) $1 \mathrm{~m} \mathrm{~s}^{-2}$
(d) $0.5 \mathrm{~m} \mathrm{~s}^{-2}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:14

Problem 173

The displacement of the body at time $\mathrm{t}=6 \mathrm{~s}$ is
(a) $6 \mathrm{~m}$
(b) $12 \mathrm{~m}$
(c) $18 \mathrm{~m}$
(d) $14 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:19

Problem 174

The magnitude of the displacement of the particle at time $\mathrm{t}=6 \mathrm{~s}$ is
(a) $12 \mathrm{~cm}$
(b) $36 \mathrm{~cm}$
(c) $24 \mathrm{~cm}$
(d) $6 \mathrm{~cm}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:04

Problem 175

The magnitude of the velocity of the particle at time $\mathrm{t}=5 \mathrm{~s}$ is
(a) zero
(b) $10 \mathrm{~cm} \mathrm{~s}^{-1}$
(c) $5 \mathrm{~cm} \mathrm{~s}^{-1}$
(d) $2.5 \mathrm{~cm} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:38

Problem 176

The acceleration of the particle at time $t=5 \mathrm{~s}$ is
(a) $2 \mathrm{~cm} \mathrm{~s}^{-2}$ along negative $\mathrm{X}$ -axis.
(b) $2 \mathrm{~cm} \mathrm{~s}^{-2}$ along positive $\mathrm{X}$ -axis.
(c) $1 \mathrm{~cm} \mathrm{~s}^{-2}$ along negative $\mathrm{X}$ -axis.
(d) $1 \mathrm{~cm} \mathrm{~s}^{-2}$ along positive $\mathrm{X}$ -axis.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:17

Problem 177

The maximum height (in $\mathrm{m}$ ) above the ground the particle rises is
(a) $48.4$
(b) $24.2$
(c) $96.8$
(d) $12.1$

Satpal Satpal
Satpal Satpal
Numerade Educator
02:05

Problem 178

The time taken to get out of the first hole is (s)
(a) $0.2$
(b) $0.3$
(c) $0.4$
(d) $0.5$

Satpal Satpal
Satpal Satpal
Numerade Educator
01:36

Problem 179

The time it moves in the second hole is (s)
(a) $0.1$
(b) $0.2$
(c) $0.3$
(d) $0.4$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:03

Problem 180

The uniform accelerations of a particle in the regions $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are $5 \mathrm{~m} \mathrm{~s}^{-2}, 5 \mathrm{~m} \mathrm{~s}^{-2}$ and 9 $\mathrm{m} \mathrm{s}^{-2}$ respectively and the thicknesses of these regions are $1.3 \mathrm{~m}, 1.1 \mathrm{~m}$ and $0.5 \mathrm{~m}$ respectively. A particle of speed $7 \mathrm{~m} \mathrm{~s}^{-1}$ enters from the left, in a direction normal to the regions A, B and C
(a) The speeds at the end of regions $A, B$ and $C$ are in the ratio $6: 5: 4$.
(b) The speeds at the end of regions $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are in the ratio $\sqrt{3}: \sqrt{2}: 1 .$
(c) The time spent in the regions $A, B$ and $C$ are in the ratio $\frac{1}{5}: \frac{1}{2.2}: 1$.
(d) The time spent in regions $A, B$ and $C$ are in the ratio $\frac{1}{5}: \frac{1}{5}: \frac{1}{9}$.

Satpal Satpal
Satpal Satpal
Numerade Educator
03:31

Problem 181

A body, which can move with constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ and constant deceleration of $4 \mathrm{~m} \mathrm{~s}^{-2}$ starts from rest at A along a straight line and stops at B and covers that total distance with maximum average velocity possible. If the distance moved during deceleration is $2 \mathrm{~m}$, then
(a) maximum velocity $=4 \mathrm{~m} \mathrm{~s}^{-1}$
(b) average velocity $=2 \mathrm{~m} \mathrm{~s}^{-1}$
(c) total distance $\mathrm{AB}=6 \mathrm{~m}$
(d) total time of travel $=4 \mathrm{~s}$

Ajay Singhal
Ajay Singhal
Numerade Educator
03:25

Problem 182

A vehicle starting from rest and moving under uniform acceleration along a straight line covers the distance between two points separated by $126 \mathrm{~m}$ in $6 \mathrm{~s}$ and the velocity at the 2 nd point is $30 \mathrm{~m} \mathrm{~s}^{-1}$. Then
(a) its velocity at first point is $12 \mathrm{~m} \mathrm{~s}^{-1}$
(b) its acceleration is $2 \mathrm{~m} \mathrm{~s}^{-2}$
(c) the first point is $22 \mathrm{~m}$ from the starting point.
(d) it reaches the first point in $4 \mathrm{~s}$ after start.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:06

Problem 183

Displacement of a particle, at the origin at $\mathrm{t}=0$, is given by $\mathrm{s}=-9 \mathrm{t}^{2}+20 \mathrm{t}$ where, $\mathrm{t}^{\prime}$ is in second and 's' in metre. Then,
(a) it will come back to origin only once.
(b) it will come back to origin with a velocity of $-20 \mathrm{~m} \mathrm{~s}^{-1}$
(c) it will come back to origin with a velocity of $+20 \mathrm{~m} \mathrm{~s}^{-1}$
(d) it will come back to origin with a velocity of $-10 \mathrm{~m} \mathrm{~s}^{-1}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:25

Problem 184

A body projected vertically up with an initial velocity $\mathrm{v}$, travels $45 \mathrm{~m}$ in the first second of its flight $\left(\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$
(a) Its initial velocity is $50 \mathrm{~m} \mathrm{~s}^{-1}$.
(b) The maximum height it reaches is $125 \mathrm{~m}$.
(c) Its time of flight is $9 \mathrm{~s}$
(d) Its time of flight is $10 \mathrm{~s}$.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:21

Problem 185

A ball thrown up vertically covers $25 \mathrm{~m}$ in its first one second of flight. Then
(a) Initial velocity $\mathrm{u}=30 \mathrm{~m} \mathrm{~s}^{-1}$
(b) Time of flight $=3 \mathrm{~s}$
(c) Maximum height $\mathrm{H}=45 \mathrm{~m}$
(d) Ratio of distance covered in the last second to the total distance of the flight is $\frac{5}{18}$

Ajay Singhal
Ajay Singhal
Numerade Educator
03:30

Problem 186

A ball thrown vertically up form the top of a tower, with a velocity of $30 \mathrm{~m} \mathrm{~s}^{-1}$ reaches ground in $8 \mathrm{~s}$. Then
(a) maximum height reached from ground is $45 \mathrm{~m}$.
(b) velocity of the ball when it reaches ground is $50 \mathrm{~m} \mathrm{~s}^{-1}$.
(c) height of the tower is $80 \mathrm{~m}$.
(d) height of the tower is $90 \mathrm{~m}$.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:14

Problem 187

A ball is dropped from a height of $60 \mathrm{~m}$. From a point vertically below on ground, a ball is projected vertically upwards with a speed of $30 \mathrm{~m} \mathrm{~s}^{-1}$ at the same instant. Then
(a) their initial relative velocity is $30 \mathrm{~m} \mathrm{~s}^{-1}$.
(b) Relative velocity at the time of collision is $40 \mathrm{~m} \mathrm{~s}^{-1}$.
(c) Time for collision is $2 \mathrm{~s}$.
(d) They collide at a height of $20 \mathrm{~m}$ from ground.

Satpal Satpal
Satpal Satpal
Numerade Educator
02:19

Problem 188

Given 'u' and 'a' in column I are constants and not equal to zero. Time is represented by ' $\mathrm{t}$ ' and position by 'x?
Column I
(a) The displacement of a particle in 1 D motion is given by $x=u(t-3)+a(t-3)^{2}$
(b) The displacement of a particle in $1 \mathrm{D}$ motion is given by $\mathrm{x}=\mathrm{ut}+\mathrm{at}^{2}$
(c) The position time graph of a body in $1 \mathrm{D}$ motion is given below
(d) $\mathrm{v}^{2}=\mathrm{u}^{2}+4$ as is the expression for the velocity of a particle in $1 \mathrm{D}$ motion where $\mathrm{s}$ is the displacement
Column II
(p) Acceleration of the particle is $2 \mathrm{a}$.
(q) The motion is uniformly accelerated.
(r) At time $\mathrm{t}=3 \mathrm{~s}$, the particle is at the origin.
(s) The particle does uniform motion.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:25

Problem 189

A man starts from rest at $\mathrm{t}=0$, on a bike to cross a point $100 \mathrm{~m}$ away on a straight road in minimum time. In the last $15 \mathrm{~m}$ of the stretch, the speed is constant at $10 \mathrm{~m} \mathrm{~s}^{-1} .$ The constant acceleration or deceleration of the bike is $10 \mathrm{~m} \mathrm{~s}^{-2} .$ Match the columns.
Column I
(a) At $\mathrm{t}=1 \mathrm{~s}$
(b) At $\mathrm{t}=3 \mathrm{~s}$
(c) At $\mathrm{t}=5 \mathrm{~s}$
(d) At $\mathrm{t}=6 \mathrm{~s}$
Column II
(p) stops deceleration
(q) $\mathrm{v}=10 \mathrm{~m} \mathrm{~s}^{-1}$
(r) $\mathrm{v}=30 \mathrm{~m} \mathrm{~s}^{-1}$
(s) $\mathrm{v}=\mathrm{v}_{\max }$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:16

Problem 190

A body is projected vertically upwards with a velocity of $40 \mathrm{~m} \mathrm{~s}^{-1}$ at $\mathrm{t}=0 .$ Match the modulus value or sign of the quantity referred in column I to the values given in column II. Take upward values as +ve.
Column I
(a) Maximum distance moved during any one second
(b) Displacement in 4 th second
(c) Distance moved in 5 th second
(d) velocity just after 3 second
Column II
(p) $\frac{\mathrm{g}}{2}$
(q) g
(r) $\frac{7 \mathrm{~g}}{2}$
$(s)+v e$

Ajay Singhal
Ajay Singhal
Numerade Educator
38:37

Problem 191

A particle moving along a straight line starts from rest at $\mathrm{t}=0$, moves with a constant acceleration of $5 \mathrm{~m} \mathrm{~s}^{-2}$ for $9 \mathrm{~s}$, then with zero acceleration for $6 \mathrm{~s}$, then with a constant acceleration of $3 \mathrm{~m} \mathrm{~s}^{-2}$ for $5 \mathrm{~s}$, then with a constant retardation of $10 \mathrm{~m} \mathrm{~s}^{-2}$ till coming to rest.
(i) Determine the time at which the instantaneous acceleration is equal to the average acceleration till that time and plot the velocity time graph.
(ii) Determine the time at which the instantaneous velocity is equal to the average velocity till that time and plot the displacement-time graph.

Robin R
Robin R
Numerade Educator
02:45

Problem 193

Three cars $A, B$ and $C$ proceed in the same direction along a straight road as detailed below, all starting from the origin. Car A was at rest at $\mathrm{t}=0$, then moving with uniform velocity of $20 \mathrm{~m} \mathrm{~s}^{-1}$. Car B started from rest at $\mathrm{t}=10 \mathrm{~s}$, with a constant acceleration of $8 \mathrm{~m} \mathrm{~s}^{-2}$. Car C was started at $\mathrm{t}=8 \mathrm{~s}$, with an initial velocity of $10 \mathrm{~m} \mathrm{~s}^{-1}$, moved with a uniform acceleration of $5 \mathrm{~m} \mathrm{~s}^{-2}$ till $\mathrm{t}=16 \mathrm{~s}$ and then was uniformly decelerating when a collision occurred, involving all three cars.
(i) At what time and at what distance from the origin did the collision occur?
(ii) What was the deceleration of car C?
(iii) Which car hit which other car from behind?

Suzanne W.
Suzanne W.
Numerade Educator
01:50

Problem 194

A ball is dropped from a height $\mathrm{h}$ on a floor where the rebound velocity is e times the impact velocity $(0<\mathrm{e}<1)$. Find the time taken by the ball to come to rest.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:05

Problem 195

Two particles are thrown from a height h. One is thrown vertically up while the other is thrown vertically down with the same speed. Analyse and plot the graph between the distance of separation and time while both bodies are moving under gravity.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:41

Problem 196

A particle is thrown up vertically from the ground with speed $\mathrm{u}$ and another particle is thrown down with the same speed at the same time from a height h. Find the minimum value of $\mathrm{u}$ so that they collide in air.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:49

Problem 197

A vessel contains a fluid to a height $\mathrm{h}_{\mathrm{f}}$ such that it exerts an additional constant retardation of a (a <g) (in addition to the gravity effects) on a ball moving in it. Find the height above the fluid surface from where the ball should be dropped so that it emerges from the fluid after collision with bottom (assume ball velocity reverses on collision with the bottom surface).

Ajay Singhal
Ajay Singhal
Numerade Educator
02:57

Problem 198

(i) A particle thrown vertically up so as to reach a maximum height $H$ in time $T$. It is at height $h$ in time $t$. Show that $\frac{t}{T}=1 \pm \sqrt{1-\frac{h}{H}}$
(ii) Particle A is thrown vertically up and after some time particle B is thrown vertically up from the same point with the same velocity. They collide 7 seconds after particle A was thrown and at a height $7 / 16$ of maximum height reached by A. What was the time interval between their projections?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:32

Problem 199

Two bodies s distance apart move towards each other with a constant velocity of $\mathrm{v}$. A particle travels with a velocity u from one body to the other and back and so on. Find the distance between the two bodies when the particle completes its nth trip (Motion from any body to the other is defined as a trip). Find the number of trips made by the particle by the time the two bodies collide. Find the distance travelled by the particle by the time the two bodies collide.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:23

Problem 200

Two cars $\mathrm{A}$ and $\mathrm{B}$ are travelling along a straight road with uniform velocities $\mathrm{v}_{\mathrm{A}}$ and $\mathrm{v}_{\mathrm{B}} . \mathrm{A}$ is behind $\mathrm{B}$ by 'd' at some instant when A applies brakes giving retardation a.
(i) Prove that the condition for no collision between the cars is $\left(\mathrm{v}_{\mathrm{A}}-\mathrm{v}_{\mathrm{B}}\right)<\sqrt{2 \mathrm{ad}}$.
(ii) Determine if a vehicle which is capable of a maximum retardation 0f $20 \mathrm{~m} \mathrm{~s}^{-2}$ and travelling at $162 \mathrm{~km} / \mathrm{h}$, will be able to avoid collision with a stationary vehicle $50 \mathrm{~m}$ in front.

Ajay Singhal
Ajay Singhal
Numerade Educator