University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

Chapter 2

Motion in a Straight Line - all with Video Answers

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Chapter Questions

Problem 1

Two athletes jump straight up. Upon leaving the ground, Adam has half the initial speed of Bob. Compared to Adam, Bob jumps
a) 0.50 times as high.
b) 1.41 times as high.
c) twice as high.
d) three times as high.
e) four times as high.

Prabhu Ramji

Prabhu Ramji

Numerade Educator

Problem 2

Two athletes jump straight up. Upon leaving the ground, Adam has half the initial speed of Bob. Compared to Adam, Bob is in the air
a) 0.50 times as long.
b) 1.41 times as long.
c) twice as long.
d) three times as long.
e) four times as long.

Prabhu Ramji

Numerade Educator

Problem 3

A car is traveling due west at $20.0 \mathrm{~m} / \mathrm{s}$. Find the velocity of the car after $3.00 \mathrm{~s}$ if its acceleration is $1.0 \mathrm{~m} / \mathrm{s}^{2}$ due west. Assume the acceleration remains constant.
a) $17.0 \mathrm{~m} / \mathrm{s}$ west
b) $17.0 \mathrm{~m} / \mathrm{s}$ east
c) $23.0 \mathrm{~m} / \mathrm{s}$ west
d) $23.0 \mathrm{~m} / \mathrm{s}$ east
e) $11.0 \mathrm{~m} / \mathrm{s}$ south

Shelby Mohamed

Numerade Educator

Problem 4

A car is traveling due west at $20.0 \mathrm{~m} / \mathrm{s}$. Find the velocity of the car after $37.00 \mathrm{~s}$ if its constant acceleration is $1.0 \mathrm{~m} / \mathrm{s}^{2}$ due east. Assume the acceleration remains constant.
a) $17.0 \mathrm{~m} / \mathrm{s}$ west
b) $17.0 \mathrm{~m} / \mathrm{s}$ east
c) $23.0 \mathrm{~m} / \mathrm{s}$ west
d) $23.0 \mathrm{~m} / \mathrm{s}$ east
e) $11.0 \mathrm{~m} / \mathrm{s}$ south

Shelby Mohamed

Numerade Educator

Problem 5

An electron, starting from rest and moving with a constant acceleration, travels $1.0 \mathrm{~cm}$ in $2.0 \mathrm{~ms}$. What is the magnitude of this acceleration?
a) $25 \mathrm{~km} / \mathrm{s}^{2}$
b) $20 \mathrm{~km} / \mathrm{s}^{2}$
c) $15 \mathrm{~km} / \mathrm{s}^{2}$
d) $10 \mathrm{~km} / \mathrm{s}^{2}$
e) $5.0 \mathrm{~km} / \mathrm{s}^{2}$

Shelby Mohamed

Numerade Educator

Problem 6

A car travels $22.0 \mathrm{~m} / \mathrm{s}$ north for $30.0 \mathrm{~min}$ and then reverses direction and travels $28.0 \mathrm{~m} / \mathrm{s}$ for $15.0 \mathrm{~min}$. What is the car's total displacement?
a) $1.44 \cdot 10^{4} \mathrm{~m}$
b) $6.48 \cdot 10^{4} \mathrm{~m}$
c) $3.96 \cdot 10^{4} \mathrm{~m}$
d) $9.98 \cdot 10^{4} \mathrm{~m}$

Pronoy Sinha

Numerade Educator

Problem 7

Which of these statement(s) is (are) true?
1. An object can have zero acceleration and be at rest.
2. An object can have nonzero acceleration and be at rest.
3. An object can have zero acceleration and be in motion.
a) 1 only
b) 1 and 3
c) 1 and 2
d) $1,2,$ and 3

Shelby Mohamed

Numerade Educator

Problem 8

A car moving at $60 \mathrm{~km} / \mathrm{h}$ comes to a stop in $4.0 \mathrm{~s}$. What was its average deceleration?
a) $2.4 \mathrm{~m} / \mathrm{s}^{2}$
b) $15 \mathrm{~m} / \mathrm{s}^{2}$
c) $4.2 \mathrm{~m} / \mathrm{s}^{2}$
d) $41 \mathrm{~m} / \mathrm{s}^{2}$

Prabhu Ramji

Numerade Educator

Problem 9

You drop a rock from a cliff. If air resistance is neglected, which of the following statements is (are) true?
1. The speed of the rock will increase.
2. The speed of the rock will decrease.
3. The acceleration of the rock will increase.
4. The acceleration of the rock will decrease.
a) 1
b) 1 and 4
c) 2
d) 2 and 3

Prabhu Ramji

Numerade Educator

Problem 10

A car travels at 22.0 mph for 15.0 min and 35.0 mph for $30.0 \mathrm{~min}$. How far does it travel overall?
a) $23.0 \mathrm{~m}$
b) $3.70 \cdot 10^{4} \mathrm{~m}$
c) $1.38 \cdot 10^{3} \mathrm{~m}$
d) $3.30 \cdot 10^{2} \mathrm{~m}$

Prabhu Ramji

Numerade Educator

Problem 11

Consider three ice skaters: Anna moves in the positive $x$ -direction without reversing. Bertha moves in the negative $x$ -direction without reversing. Christine moves in the positive $x$ -direction and then reverses the direction of her motion. For which of these skaters is the magnitude of the average velocity smaller than the average speed over some time interval?

Prabhu Ramji

Numerade Educator

Problem 12

You toss a small ball vertically up in the air. How are the velocity and acceleration vectors of the ball oriented with respect to one another during the ball's flight up and down?

Shelby Mohamed

Numerade Educator

Problem 13

After you apply the brakes, the acceleration of your car is in the opposite direction to its velocity. If the acceleration of your car remains constant, describe the motion of your car.

Prabhu Ramji

Numerade Educator

Problem 14

Two cars are traveling at the same speed, and the drivers hit the brakes at the same time. The deceleration of one car is double that of the other. By what factor does the time required for that car to come to a stop compare with that for the other car?

Shelby Mohamed

Numerade Educator

Problem 15

If the acceleration of an object is zero and its velocity is nonzero, what can you say about the motion of the object? Sketch velocity versus time and acceleration versus time graphs for your explanation.

Shelby Mohamed

Numerade Educator

Problem 16

Can an object's acceleration be in the opposite direction to its motion? Explain.

Shelby Mohamed

Numerade Educator

Problem 17

You and a friend are standing at the edge of a snowcovered cliff. At the same time, you both drop a snowball over the edge of the cliff. Your snowball is twice as heavy as your friend's. Neglect air resistance.
(a) Which snowball will hit the ground first?
(b) Which snowball will have the greater speed?

Shelby Mohamed

Numerade Educator

Problem 18

You and a friend are standing at the edge of a snowcovered cliff. At the same time, you throw a snowball straight upward with a speed of $8.0 \mathrm{~m} / \mathrm{s}$ over the edge of the cliff and your friend throws a snowball straight downward over the edge of the cliff with the same speed. Your snowball is twice as heavy as your friend's. Neglecting air resistance, which snowball will hit the ground first, and which will have the greater speed?

Shelby Mohamed

Numerade Educator

Problem 19

A car is slowing down and comes to a complete stop. The figure shows an image sequence of this process. The time between successive frames is $0.333 \mathrm{~s},$ and the car is the same as the one in Solved Problem 2.5. Assuming constant acceleration, what is its value? Can you give some estimate of the error in your answer? How well justified is the assumption of constant acceleration?

Shelby Mohamed

Numerade Educator

Problem 20

A car moves along a road with a constant velocity. Starting at time $t=2.5 \mathrm{~s}$, the driver accelerates with constant acceleration. The resulting position of the car as a function of time is shown by the blue curve in the figure
a) What is the value of the constant velocity of the car before 2.5 s? (Hint: The dashed blue line is the path the car would take in the absence of the acceleration.)
b) What is the velocity of the car at $t=7.5$ s? Use a graphical technique (i.e., draw a slope).
c) What is the value of the constant acceleration?
.

Shelby Mohamed

Numerade Educator

Problem 21

You drop a rock over the edge of a cliff from a height $h$. Your friend throws a rock over the edge from the same height with a speed $v_{0}$ vertically downward, at some time $t$ after you drop your rock. Both rocks hit the ground at the same time. How long after you dropped your rock did your friend throw hers? Express your answer in terms of $v_{0}, g,$ and $h$.

Prabhu Ramji

Numerade Educator

Problem 22

The position of a particle as a function of time is given as $x(t)=\frac{1}{4} x_{0} e^{3 \alpha t}$, where $\alpha$ is a positive constant.
a) At what time is the particle at $2 x_{0}$ ?
b) What is the speed of the particle as a function of time?
c) What is the acceleration of the particle as a function of time?
d) What are the SI units for $\alpha$ ?

Tyler Moulton

Numerade Educator

Problem 23

The position versus time for an object is given as $x=A t^{4}-B t^{3}+C$
a) What is the instantaneous velocity as a function of time?
b) What is the instantaneous acceleration as a function of time?

Shelby Mohamed

Numerade Educator

Problem 24

A wrench is thrown vertically upward with speed $v_{0}$. How long after its release is it halfway to its maximum height?

Prabhu Ramji

Numerade Educator

Problem 25

A car travels north at $30.0 \mathrm{~m} / \mathrm{s}$ for $10.0 \mathrm{~min}$. It then travels south at $40.0 \mathrm{~m} / \mathrm{s}$ for $20.0 \mathrm{~min}$. What are the total distance the car travels and its displacement?

Prabhu Ramji

Numerade Educator

Problem 26

You ride your bike along a straight line from your house to a store $1000 .$ m away. On your way back, you stop at a friend's house which is halfway between your house and the store.
a) What is your displacement?
b) What is the total distance traveled? After talking to your friend, you continue to your house. When you arrive back at your house,
c) What is your displacement?
d) What is the distance you have traveled?

Prabhu Ramji

Numerade Educator

Problem 27

Running along a rectangular track $50 \mathrm{~m} \times 40 \mathrm{~m}$ you complete one lap in $100 \mathrm{~s}$. What is your average velocity for the lap?

Shelby Mohamed

Numerade Educator

Problem 28

An electron moves in the positive $x$ -direction a distance of $2.42 \mathrm{~m}$ in $2.91 \cdot 10^{-8} \mathrm{~s}$, bounces off a moving proton, and then moves in the opposite direction a distance of $1.69 \mathrm{~m}$ in $3.43 \cdot 10^{-8} \mathrm{~s}$.
a) What is the average velocity of the electron over the entire time interval?
b) What is the average speed of the electron over the entire time interval?

Prabhu Ramji

Numerade Educator

Problem 29

The graph describes the position of a particle in one dimension as a function of time. Answer the following questions.
a) In which time interval does the particle have its maximum speed? What is that speed?
b) What is the average velocity in the time interval between $-5 \mathrm{~s}$
and $+5 \mathrm{~s} ?$
c) What is the average speed in the time interval between $-5 \mathrm{~s}$ and $+5 \mathrm{~s} ?$
d) What is the ratio of the velocity in the interval between $2 \mathrm{~s}$ and 3 s to that in the interval between $3 \mathrm{~s}$ and $4 \mathrm{~s} ?$
e) At what time(s) is the particle's velocity zero?

Supratim Pal

Numerade Educator

Problem 30

The position of a particle moving along the $x$ -axis is given by $x=\left(11+14 t-2.0 t^{2}\right),$ where $t$ is in seconds and $x$ is in meters. What is the average velocity during the time interval from $t=1.0 \mathrm{~s}$ to $t=4.0 \mathrm{~s} ?$

Prabhu Ramji

Numerade Educator

Problem 31

The position of a particle moving along the $x$ -axis is given by $x=3.0 t^{2}-2.0 t^{3},$ where $x$ is in meters and $t$ is in seconds. What is the position of the particle when it achieves its maximum speed in the positive $x$ -direction?

Prabhu Ramji

Numerade Educator

Problem 32

The rate of continental drift is on the order of $10.0 \mathrm{~mm} / \mathrm{yr}$. Approximately how long did it take North America and Europe to reach their current separation of about $3000 \mathrm{mi}$ ?

Prabhu Ramji

Numerade Educator

Problem 33

You and a friend are driving to the beach during spring break. You travel $16.0 \mathrm{~km}$ east and then $80.0 \mathrm{~km}$ south in a total time of 40.0 minutes.
(a) What is the average speed of the trip? (b) What is the average velocity?

Shelby Mohamed

Numerade Educator

Problem 34

The trajectory of an object is given by the equation
$$
x(t)=(4.35 \mathrm{~m})+(25.9 \mathrm{~m} / \mathrm{s}) t-\left(11.79 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}
$$

a) For which time $t$ is the displacement $x(t)$ at its maximum?
b) What is this maximum value?

Prabhu Ramji

Numerade Educator

Problem 35

A bank robber in a getaway car approaches an intersection at a speed of 45 mph. Just as he passes the intersection, he realizes that he needed to turn. So he steps on the brakes, comes to a complete stop, and then accelerates driving straight backward. He reaches a speed of $22.5 \mathrm{mph}$ moving backward. Altogether his deceleration and reacceleration in the opposite direction take $12.4 \mathrm{~s} .$ What is the average acceleration during this time?

Shelby Mohamed

Numerade Educator

Problem 36

A car is traveling west at $22.0 \mathrm{~m} / \mathrm{s}$. After $10.0 \mathrm{~s}$, its velocity is $17.0 \mathrm{~m} / \mathrm{s}$ in the same direction. Find the magnitude and direction of the car's average acceleration.

Prabhu Ramji

Numerade Educator

Problem 37

Your friend's car starts from rest and travels $0.500 \mathrm{~km}$
in $10.0 \mathrm{~s}$. What is the magnitude of the constant acceleration required to do this?

Shelby Mohamed

Numerade Educator

Problem 38

A fellow student found in the performance data for his new car the velocity-versus-time graph shown in the figure.
a) Find the average acceleration of the car during each of the segments I, II, and III.
b) What is the total distance traveled by the car from $t=0$ s to $t=24 \mathrm{~s} ?$

Prabhu Ramji

Numerade Educator

Problem 39

The velocity of a particle moving along the $x$ -axis is given, for $t>0$, by $v_{x}=\left(50.0 t-2.0 t^{3}\right) \mathrm{m} / \mathrm{s}$, where $t$ is in seconds. What is the acceleration of the particle when (after $t=0$ ) it achieves its maximum displacement in the positive $x$ -direction?

Prabhu Ramji

Numerade Educator

Problem 40

The 2007 world record for the men's 100 -m dash was $9.77 \mathrm{~s}$. The third-place runner crossed the finish line in $10.07 \mathrm{~s}$. When the winner crossed the finish line, how far was the third-place runner behind him?
a) Compute an answer that assumes that each runner ran at his average speed for the entire race.
b) Compute another answer that uses the result of Example 2.3, that a world-class sprinter runs at a speed of $12 \mathrm{~m} / \mathrm{s}$ after an initial acceleration phase. If both runners in this race reach this speed, how far behind is the third-place runner when the winner finishes?

Vedad Babic

Numerade Educator

Problem 41

The position of an object as a function of time is given as $x=A t^{3}+B t^{2}+C t+D .$ The constants are $A=2.1 \mathrm{~m} / \mathrm{s}^{3}$
$B=1.0 \mathrm{~m} / \mathrm{s}^{2}, C=-4.1 \mathrm{~m} / \mathrm{s},$ and $D=3 \mathrm{~m}$
a) What is the velocity of the object at $t=10.0 \mathrm{~s}$ ?
b) At what time(s) is the object at rest?
c) What is the acceleration of the object at $t=0.50 \mathrm{~s} ?$
d) Plot the acceleration as a function of time for the time interval from $t=-10.0 \mathrm{~s}$ to $t=10.0 \mathrm{~s}$.

Shelby Mohamed

Numerade Educator

Problem 42

An F-14 Tomcat fighter jet is taking off from the deck of the USS Nimitz aircraft carrier with the assistance of
a steam-powered catapult. The jet's location along the flight deck is measured at intervals of $0.20 \mathrm{~s} .$ These measurements are tabulated as follows:
$$
\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline t(\mathrm{~s}) & 0.00 & 0.20 & 0.40 & 0.60 & 0.80 & 1.00 & 1.20 & 1.40 & 1.60 & 1.80 & 2.00 \\
\hline x(\mathrm{~m}) & 0.0 & 0.70 & 3.0 & 6.6 & 11.8 & 18.5 & 26.6 & 36.2 & 47.3 & 59.9 & 73.9 \\
\hline
\end{array}
$$
Use difference formulas to calculate the jet's average velocity and average acceleration for each time interval. After completing this analysis, can you say if the F- 14 Tomcat accelerated with approximately constant acceleration?

Vedad Babic

Numerade Educator

Problem 43

A particle starts from rest at $x=0$ and moves for $20 \mathrm{~s}$ with an acceleration of $+2.0 \mathrm{~cm} / \mathrm{s}^{2}$. For the next $40 \mathrm{~s}$, the acceleration of the particle is $-4.0 \mathrm{~cm} / \mathrm{s}^{2} .$ What is the position of the particle at the end of this motion?

Vishal Gupta

Numerade Educator

Problem 44

A car moving in the $x$ -direction has an acceleration $a_{x}$ that varies with time as shown in the figure. At the moment $t=0 \mathrm{~s}$, the car is located at $x=12 \mathrm{~m}$ and has a velocity of $6 \mathrm{~m} / \mathrm{s}$ in the positive $x$ -direction. What is the velocity of the car at $t=5.0 \mathrm{~s} ?$

Prabhu Ramji

Numerade Educator

Problem 45

The velocity as a function of time for a car on an amusement park ride is given as $v=A t^{2}+B t$ with constants $A=2.0 \mathrm{~m} / \mathrm{s}^{3}$ and $B=1.0 \mathrm{~m} / \mathrm{s}^{2} .$ If the car starts at the origin, what is its position at $t=3.0$ s?

Prabhu Ramji

Numerade Educator

Problem 46

An object starts from rest and has an acceleration given by $a=B t^{2}-\frac{1}{2} C t,$ where $B=2.0 \mathrm{~m} / \mathrm{s}^{4}$ and $C=-4.0 \mathrm{~m} / \mathrm{s}^{3}$.
a) What is the object's velocity after 5.0 s?
b) How far has the object moved after $t=5.0$ s?

Prabhu Ramji

Numerade Educator

Problem 47

A car is moving along the $x$ -axis and its velocity, $v_{x}$ varies with time as shown in the figure. If $x_{0}=2.0 \mathrm{~m}$ at $t_{0}=$ $2.0 \mathrm{~s}$, what is the position of the car at $t=10.0 \mathrm{~s} ?$

Prabhu Ramji

Numerade Educator

Problem 48

A car is moving along the $x$ -axis and its velocity, $v_{x}$ varies with time as shown in the figure. What is the displacement, $\Delta x$, of the car from $t=4$ s to $t=9$ s?

Prabhu Ramji

Numerade Educator

Problem 49

A motorcycle starts from rest and accelerates as shown in the figure. Determine (a) the motorcycle's speed at $t=4.00 \mathrm{~s}$ and at $t=14.0 \mathrm{~s},$ and $(\mathrm{b})$ the distance traveled in the first $14.0 \mathrm{~s}$.

Prabhu Ramji

Numerade Educator

Problem 50

How much time does it take for a car to accelerate from a standing start to $22.2 \mathrm{~m} / \mathrm{s}$ if the acceleration is constant and the car covers $243 \mathrm{~m}$ during the acceleration?

Prabhu Ramji

Numerade Educator

Problem 51

A car slows down from a speed of $31.0 \mathrm{~m} / \mathrm{s}$ to a speed of $12.0 \mathrm{~m} / \mathrm{s}$ over a distance of $380 . \mathrm{m} .$
a) How long does this take, assuming constant acceleration?
b) What is the value of this acceleration?

Prabhu Ramji

Numerade Educator

Problem 52

A runner of mass 57.5 kg starts from rest and accelerates with a constant acceleration of $1.25 \mathrm{~m} / \mathrm{s}^{2}$ until she reaches a velocity of $6.3 \mathrm{~m} / \mathrm{s}$. She then continues running with this constant velocity.
a) How far has she run after 59.7 s?
b) What is the velocity of the runner at this point?

Prabhu Ramji

Numerade Educator

Problem 53

A fighter jet lands on the deck of an aircraft carrier. It touches down with a speed of $70.4 \mathrm{~m} / \mathrm{s}$ and comes to a complete stop over a distance of $197.4 \mathrm{~m}$. If this process happens with constant deceleration, what is the speed of the jet $44.2 \mathrm{~m}$ before its final stopping location?

Prabhu Ramji

Numerade Educator

Problem 54

A bullet is fired through a board $10.0 \mathrm{~cm}$ thick, with a line of motion perpendicular to the face of the board. If the bullet enters with a speed of $400 . \mathrm{m} / \mathrm{s}$ and emerges with a speed of $200 . \mathrm{m} / \mathrm{s}$, what is its acceleration as it passes through the board?

Prabhu Ramji

Numerade Educator

Problem 55

A car starts from rest and accelerates at $10.0 \mathrm{~m} / \mathrm{s}^{2}$ How far does it travel in 2.00 s?

Prabhu Ramji

Numerade Educator

Problem 56

An airplane starts from rest and accelerates at $12.1 \mathrm{~m} / \mathrm{s}^{2}$. What is its speed at the end of a $500 .-\mathrm{m}$ runway?

Prabhu Ramji

Numerade Educator

Problem 57

Starting from rest, a boat increases its speed to $5.00 \mathrm{~m} / \mathrm{s}$ with constant acceleration.
a) What is the boat's average speed?
b) If it takes the boat 4.00 s to reach this speed, how far has it traveled?

Prabhu Ramji

Numerade Educator

Problem 58

A ball is tossed vertically upward with an initial speed of $26.4 \mathrm{~m} / \mathrm{s}$. How long does it take before the ball is back on the ground?

Prabhu Ramji

Numerade Educator

Problem 59

A stone is thrown upward, from ground level, with an initial velocity of $10.0 \mathrm{~m} / \mathrm{s}$.
a) What is the velocity of the stone after 0.50 s?
b) How high above ground level is the stone after 0.50 s?

Prabhu Ramji

Numerade Educator

Problem 60

A stone is thrown downward with an initial velocity of $10.0 \mathrm{~m} / \mathrm{s}$. The acceleration of the stone is constant and has the value of the free-fall acceleration, $9.81 \mathrm{~m} / \mathrm{s}^{2} .$ What is the velocity of the stone after $0.500 \mathrm{~s} ?$

Prabhu Ramji

Numerade Educator

Problem 61

A ball is thrown directly downward, with an initial speed of $10.0 \mathrm{~m} / \mathrm{s}$, from a height of $50.0 \mathrm{~m}$. After what time interval does the ball strike the ground?

Prabhu Ramji

Numerade Educator

Problem 62

An object is thrown vertically upward and has a speed of $20.0 \mathrm{~m} / \mathrm{s}$ when it reaches two thirds of its maximum height above the launch point. Determine its maximum height.

Prabhu Ramji

Numerade Educator

Problem 63

What is the velocity at the midway point of a ball able to reach a height $y$ when thrown with an initial velocity $v_{0} ?$

Shelby Mohamed

Numerade Educator

Problem 64

Runner 1 is standing still on a straight running track. Runner 2 passes him, running with a constant speed of $5.1 \mathrm{~m} / \mathrm{s} .$ Just as runner 2 passes, runner 1 accelerates with a constant acceleration of $0.89 \mathrm{~m} / \mathrm{s}^{2} .$ How far down the track
does runner 1 catch up with runner $2 ?$

Prabhu Ramji

Numerade Educator

Problem 65

A girl is riding her bicycle. When she gets to a corner, she stops to get a drink from her water bottle. At that time, a friend passes by her, traveling at a constant speed of $8.0 \mathrm{~m} / \mathrm{s}$.
a) After $20 \mathrm{~s}$, the girl gets back on her bike and travels with a constant acceleration of $2.2 \mathrm{~m} / \mathrm{s}^{2} .$ How long does it take for her to catch up with her friend?
b) If the girl had been on her bike and rolling along at a speed of $1.2 \mathrm{~m} / \mathrm{s}$ when her friend passed, what constant acceleration would she need to catch up with her friend in the same amount of time?

Prabhu Ramji

Numerade Educator

Problem 66

A speeding motorcyclist is traveling at a constant speed of $36.0 \mathrm{~m} / \mathrm{s}$ when he passes a police car parked on the side of the road. The radar, positioned in the police car's rear window, measures the speed of the motorcycle. At the instant the motorcycle passes the police car, the police officer starts to chase the motorcyclist with a constant acceleration of $4.0 \mathrm{~m} / \mathrm{s}^{2}$
a) How long will it take the police officer to catch the motorcyclist?
b) What is the speed of the police car when it catches up to the motorcycle?
c) How far will the police car be from its original position?

Vishal Gupta

Numerade Educator

Problem 67

Two train cars are on a straight, horizontal track. One car starts at rest and is put in motion with a constant acceleration of $2.00 \mathrm{~m} / \mathrm{s}^{2}$. This car moves toward a second car that is
$30.0 \mathrm{~m}$ away and moving at a constant speed of $4.00 \mathrm{~m} / \mathrm{s}$.
a) Where will the cars collide?
b) How long will it take for the cars to collide?

Shelby Mohamed

Numerade Educator

Problem 68

The planet Mercury has a mass that is $5 \%$ of that of Earth, and its gravitational acceleration is $g_{\text {mercury }}=3.7 \mathrm{~m} / \mathrm{s}^{2}$
a) How long does it take for a rock that is dropped from a height of $1.75 \mathrm{~m}$ to hit the ground on Mercury?
b) How does this time compare to the time it takes the same rock to reach the ground on Earth, if dropped from the same height?
c) From what height would you have to drop the rock on Earth so that the fall-time on both planets is the same?

Shelby Mohamed

Numerade Educator

Problem 69

Bill Jones has a bad night in his bowling league. When he gets home, he drops his bowling ball in disgust out the window of his apartment, from a height of $63.17 \mathrm{~m}$ above the ground. John Smith sees the bowling ball pass by his window when it is $40.95 \mathrm{~m}$ above the ground. How much time passes from the time when John Smith sees the bowling ball pass his window to when it hits the ground?

Shelby Mohamed

Numerade Educator

Problem 70

Picture yourself in the castle of Helm's Deep from the Lord of the Rings. You are on top of the castle wall and are dropping rocks on assorted monsters that are $18.35 \mathrm{~m}$ below you. Just when you release a rock, an archer located exactly below you shoots an arrow straight up toward you with an initial velocity of $47.4 \mathrm{~m} / \mathrm{s}$. The arrow hits the rock in midair. How long after you release the rock does this happen?

Vishal Gupta

Numerade Educator

Problem 71

An object is thrown vertically and has an upward velocity of $25 \mathrm{~m} / \mathrm{s}$ when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?

Prabhu Ramji

Numerade Educator

Problem 72

In a fancy hotel, the back of the elevator is made of glass so that you can enjoy a lovely view on your ride. The elevator travels at an average speed of $1.75 \mathrm{~m} / \mathrm{s}$. A boy on the 15th floor, $80.0 \mathrm{~m}$ above the ground level, drops a rock at the same instant the elevator starts its ascent from the 1st to the 5th floor. Assume the elevator travels at its average speed for the entire trip and neglect the dimensions of the elevator.
a) How long after it was dropped do you see the rock?
b) How long does it take for the rock to reach ground level?

Prabhu Ramji

Numerade Educator

Problem 73

You drop a water balloon straight down from your dormitory window $80.0 \mathrm{~m}$ above your friend's head. At $2.00 \mathrm{~s}$ after you drop the balloon, not realizing it has water in it your friend fires a dart from a gun, which is at the same height as his head, directly upward toward the balloon with an initial velocity of $20.0 \mathrm{~m} / \mathrm{s}$.
a) How long after you drop the balloon will the dart burst the balloon?
b) How long after the dart hits the balloon will your friend have to move out of the way of the falling water? Assume the balloon breaks instantaneously at the touch of the dart.

Supratim Pal

Numerade Educator

Problem 74

A runner of mass $56.1 \mathrm{~kg}$ starts from rest and accelerates with a constant acceleration of $1.23 \mathrm{~m} / \mathrm{s}^{2}$ until she reaches a velocity of $5.10 \mathrm{~m} / \mathrm{s}$. She then continues running at this constant velocity. How long does the runner take to travel $173 \mathrm{~m} ?$

Prabhu Ramji

Numerade Educator

Problem 75

A jet touches down on a runway with a speed of $142.4 \mathrm{mph} .$ After $12.4 \mathrm{~s},$ the jet comes to a complete stop. Assuming constant acceleration of the jet, how far down the runway from where it touched down does the jet stand?

Prabhu Ramji

Numerade Educator

Problem 76

On the graph of position as a function of time, mark the points where the velocity is zero, and the points where the acceleration is zero.

Shelby Mohamed

Numerade Educator

Problem 77

An object is thrown upward with a speed of $28.0 \mathrm{~m} / \mathrm{s}$. How long does it take it to reach its maximum height?

Prabhu Ramji

Numerade Educator

Problem 78

An object is thrown upward with a speed of $28.0 \mathrm{~m} / \mathrm{s}$. How high above the projection point is it after 1.00 s?

Prabhu Ramji

Numerade Educator

Problem 79

An object is thrown upward with a speed of $28.0 \mathrm{~m} / \mathrm{s}$. What maximum height above the projection point does it reach?

Nishant Kumar

Numerade Educator

Problem 80

The minimum distance necessary for a car to brake to a stop from a speed of $100.0 \mathrm{~km} / \mathrm{h}$ is $40.00 \mathrm{~m}$ on a dry pavement. What is the minimum distance necessary for this car to brake to a stop from a speed of $130.0 \mathrm{~km} / \mathrm{h}$ on dry pavement?

Prabhu Ramji

Numerade Educator

Problem 81

A car moving at $60.0 \mathrm{~km} / \mathrm{h}$ comes to a stop in $t=4.00 \mathrm{~s}$ Assume uniform deceleration.
a) How far does the car travel while stopping?
b) What is its deceleration?

Prabhu Ramji

Numerade Educator

Problem 82

You are driving at $29.1 \mathrm{~m} / \mathrm{s}$ when the truck ahead of you comes to a halt $200.0 \mathrm{~m}$ away from your bumper. Your brakes are in poor condition and you decelerate at a constant rate of $2.4 \mathrm{~m} / \mathrm{s}^{2}$
a) How close do you come to the bumper of the truck?
b) How long does it take you to come to a stop?

Prabhu Ramji

Numerade Educator

Problem 83

A train traveling at $40.0 \mathrm{~m} / \mathrm{s}$ is headed straight toward another train, which is at rest on the same track. The moving train decelerates at $6.0 \mathrm{~m} / \mathrm{s}^{2},$ and the stationary train is $100.0 \mathrm{~m}$ away. How far from the stationary train will the moving train be when it comes to a stop?

Prabhu Ramji

Numerade Educator

Problem 84

A car traveling at $25.0 \mathrm{~m} / \mathrm{s}$ applies the brakes and decelerates uniformly at a rate of $1.2 \mathrm{~m} / \mathrm{s}^{2}$
a) How far does it travel in $3.0 \mathrm{~s}$ ?
b) What is its velocity at the end of this time interval?
c) How long does it take for the car to come to a stop?
d) What distance does the car travel before coming to a stop?

Shelby Mohamed

Numerade Educator

Problem 85

The fastest speed in NASCAR racing history was $212.809 \mathrm{mph}$ (reached by Bill Elliott in 1987 at Talladega). If the race car decelerated from that speed at a rate of $8.0 \mathrm{~m} / \mathrm{s}^{2},$ how far would it travel before coming to a stop?

Prabhu Ramji

Numerade Educator

Problem 86

You are flying on a commercial airline on your way from Houston, Texas, to Oklahoma City, Oklahoma. Your pilot announces that the plane is directly over Austin, Texas, traveling at a constant speed of $245 \mathrm{mph}$, and will be flying directly over Dallas, Texas, $362 \mathrm{~km}$ away. How long will it be before you are directly over Dallas, Texas?

Prabhu Ramji

Numerade Educator

Problem 87

The position of a race car on a straight track is given as $x=a t^{3}+b t^{2}+c,$ where $a=2.0 \mathrm{~m} / \mathrm{s}^{3}, b=2.0 \mathrm{~m} / \mathrm{s}^{2}$, and $c=3.0 \mathrm{~m}$.
a) What is the car's position between $t=4.0 \mathrm{~s}$ and $t=9.0 \mathrm{~s}$ ?
b) What is the average speed between $t=4.0 \mathrm{~s}$ and $t=9.0 \mathrm{~s} ?$

Shelby Mohamed

Numerade Educator

Problem 88

A girl is standing at the edge of a cliff $100 . \mathrm{m}$ above the ground. She reaches out over the edge of the cliff and throws a rock straight upward with a speed $8.00 \mathrm{~m} / \mathrm{s}$.
a) How long does it take the rock to hit the ground?
b) What is the speed of the rock the instant before it hits the ground?

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 89

A double speed trap is set up on a freeway. One police cruiser is hidden behind a billboard, and another is some distance away under a bridge. As a sedan passes by the first cruiser, its speed is measured to be $105.9 \mathrm{mph}$. Since the driver has a radar detector, he is alerted to the fact that his speed has been measured, and he tries to slow his car down gradually without stepping on the brakes and alerting the police that he knew he was going too fast. Just taking the foot off the gas leads to a constant deceleration. Exactly 7.05 s later the sedan passes the second police cruiser. Now its speed is measured to be only $67.1 \mathrm{mph}$, just below the local freeway speed limit.
a) What is the value of the deceleration?
b) How far apart are the two cruisers?

Prabhu Ramji

Numerade Educator

Problem 90

During a test run on an airport runway, a new race car reaches a speed of 258.4 mph from a standing start. The car accelerates with constant acceleration and reaches this speed mark at a distance of $612.5 \mathrm{~m}$ from where it started. What was its speed after one-fourth, one-half, and three-fourths of this distance?

Tyler Moulton

Numerade Educator

Problem 91

The vertical position of a ball suspended by a rubber band is given by the equation
$$
y(t)=(3.8 \mathrm{~m}) \sin (0.46 t / \mathrm{s}-0.31)-(0.2 \mathrm{~m} / \mathrm{s}) t+5.0 \mathrm{~m}
$$
a) What are the equations for velocity and acceleration for this ball?
b) For what times between 0 and $30 \mathrm{~s}$ is the acceleration zero?

Tyler Moulton

Numerade Educator

Problem 92

The position of a particle moving along the $x$ -axis varies with time according to the expression $x=4 t^{2},$ where $x$ is in meters and $t$ is in seconds. Evaluate the particle's position
a) at $t=2.00 \mathrm{~s}$.
b) at $2.00 \mathrm{~s}+\Delta t$
c) Evaluate the limit of $\Delta x / \Delta t$ as $\Delta t$ approaches zero, to find the velocity at $t=2.00 \mathrm{~s}$.

Shelby Mohamed

Numerade Educator

Problem 93

In 2005, Hurricane Rita hit several states in the southern United States. In the panic to escape her wrath, thousands of people tried to flee Houston, Texas by car. One car full of college students traveling to Tyler, Texas, 199 miles north of Houston, moved at an average speed of $3.0 \mathrm{~m} / \mathrm{s}$ for one-fourth of the time, then at $4.5 \mathrm{~m} / \mathrm{s}$ for another one-fourth of the time, and at $6.0 \mathrm{~m} / \mathrm{s}$ for the remainder of the trip.
a) How long did it take the students to reach their destination?
b) Sketch a graph of position versus time for the trip.

Shelby Mohamed

Numerade Educator

Problem 94

A ball is thrown straight upward in the air at a speed of $15.0 \mathrm{~m} / \mathrm{s} .$ Ignore air resistance.
a) What is the maximum height the ball will reach?
b) What is the speed of the ball when it reaches $5.00 \mathrm{~m} ?$
c) How long will it take to reach $5.00 \mathrm{~m}$ above its initial position on the way up?
d) How long will it take to reach $5.00 \mathrm{~m}$ above its initial position on its way down?

Tyler Moulton

Numerade Educator

Problem 95

The Bellagio Hotel in Las Vegas, Nevada, is well known for its Musical Fountains, which use 192 HyperShooters to fire water hundreds of feet into the air to the rhythm of music. One of the HyperShooters fires water straight upward to a height of $240 \mathrm{ft}$.
a) What is the initial speed of the water?
b) What is the speed of the water when it is at half this height on its way down?
c) How long will it take for the water to fall back to its original height from half its maximum height?

Vedad Babic

Numerade Educator

Problem 96

You are trying to improve your shooting skills by shooting at a can on top of a fence post. You miss the can, and the bullet, moving at $200 . \mathrm{m} / \mathrm{s},$ is embedded $1.5 \mathrm{~cm}$ into the post when it comes to a stop. If constant acceleration is assumed, how long does it take for the bullet to stop?

Prabhu Ramji

Numerade Educator

Problem 97

You drive with a constant speed of $13.5 \mathrm{~m} / \mathrm{s}$ for 30.0 s. You then accelerate for 10.0 s to a speed of $22.0 \mathrm{~m} / \mathrm{s}$. You then slow to a stop in $10.0 \mathrm{~s}$. How far have you traveled?

Shelby Mohamed

Numerade Educator

Problem 98

A ball is dropped from the roof of a building. It hits the ground and it is caught at its original height 5.0 s later.
a) What was the speed of the ball just before it hits the ground?
b) How tall was the building?
c) You are watching from a window $2.5 \mathrm{~m}$ above the ground. The window opening is $1.2 \mathrm{~m}$ from the top to the bottom. At what time after the ball was dropped did you first see the ball in the window?

Shelby Mohamed

Numerade Educator