Understanding Physics

Karen Cummings, Priscilla W. Laws, Edward F. Redish

Chapter 2

Motion Along a Straight Line - all with Video Answers

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Chapter Questions

Problem 1

If a baseball pitcher throws a fastball at a horizontal speed of $160 \mathrm{~km} / \mathrm{h}$, how long does the ball take to reach home plate $18.4 \mathrm{~m}$ away?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 2

A world speed record for bicycles was set in 1992 by Chris Huber riding Cheetah, a high-tech bicycle built by three mechanical engineering graduates. The record (average) speed was $110.6 \mathrm{~km} / \mathrm{h}$ through a measured length of $200.0 \mathrm{~m}$ on a desert road. At the end of the run, Huber commented, "Cogito ergo zoom!" (I think, therefore I go fast!) What was Huber's elapsed time through the $200.0 \mathrm{~m}$ ?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 3

An automobile travels on a straight road for $40 \mathrm{~km}$ at $30 \mathrm{~km} / \mathrm{h}$. It then continues in the same direction for another $40 \mathrm{~km}$ at $60 \mathrm{~km} / \mathrm{h}$. (a) What is the average velocity of the car during this $80 \mathrm{~km}$ trip? (Assume that it moves in the positive $x$ direction.)
(b) What is the average speed?
(c) Graph $x$ vs. $t$ and indicate how the average velocity is found on the graph.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 4

A top-gun pilot, practicing radar avoidance maneuvers, is manually flying horizontally at $1300 \mathrm{~km} / \mathrm{h}$, just $35 \mathrm{~m}$ above the level ground. Suddenly, the plane encounters terrain that slopes gently upward at $4.3^{\circ}$, an amount difficult to detect visually (Fig. 2-22). How much time does the pilot have to make a correction to avoid flying into the ground?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 5

You drive on Interstate 10 from San Antonio to Houston, half the time at $55 \mathrm{~km} / \mathrm{h}$ and the other half at $90 \mathrm{~km} / \mathrm{h}$. On the way back you travel half the distance at $55 \mathrm{~km} / \mathrm{h}$ and the other half at $90 \mathrm{~km} / \mathrm{h}$. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and
(c) for the entire trip? (d) What is your average velocity for the entire trip? (c) Sketch $x$ vs. $t$ for (a), assuming the motion is all in the positive $x$ direction. Indicate how the average velocity can be found on the sketch.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 6

Compute your average velocity in the following two cases: (a) You walk $73.2 \mathrm{~m}$ at a speed of $1.22 \mathrm{~m} / \mathrm{s}$ and then run $73.2 \mathrm{~m}$ at a speed of $3.05 \mathrm{~m} / \mathrm{s}$ along a straight track. (b) You walk for $1.00 \mathrm{~min}$ at a speed of $1.22 \mathrm{~m} / \mathrm{s}$ and then run for $1.00 \mathrm{~min}$ at $3.05 \mathrm{~m} / \mathrm{s}$
along a straight track. (c) Graph $x$ vs. $t$ for both cases and indicate how the average velocity is found on the graph.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 7

The position of an object moving along an $x$ axis is given by $x=(3 \mathrm{~m} / \mathrm{s}) t-\left(4 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}+\left(1 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}$, where $x$ is in
meters and $t$ in seconds. (a) What is the position of the object at $t=$ $1,2,3$, and $4 \mathrm{~s}$ ? (b) What is the object's displacement between $t_{1}=0 \mathrm{~s}$ and $t_{2}=4 \mathrm{~s} ?(\mathrm{c})$ What is the average velocity between the time in-
(d) Graph $x$ vs. $t$ for $0 \leq t \leq 4 \mathrm{~s}$ and terval from $t_{1}=2 \mathrm{~s}$ to $t_{2}=4 \mathrm{~s} ?$ indicate how the answer for (c) can be found on the graph.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 8

Two trains, each having a speed of $30 \mathrm{~km} / \mathrm{h}$, are headed at each other on the same straight track. A bird that can fly $60 \mathrm{~km} / \mathrm{h}$ flies off the front of one train when they are $60 \mathrm{~km}$ apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 9

On two different tracks, the winners of the 1 kilomcter race ran their races in $2 \mathrm{~min}, 27.95 \mathrm{~s}$ and $2 \mathrm{~min}, 28.15 \mathrm{~s}$. In order to conclude that the runner with the shorter time was indeed faster, how much longer can the other track be in actual length?

John Biddulph

Numerade Educator

Problem 10

The graph in Fig. $2-23$ is for an armadillo that scampers left (negative direction of $x$ ) and right along an $x$ axis.
(a) When, if ever, is the animal to the left of the origin on the axis? When. if ever, is its velocity component (b) negative, $(\mathrm{c})$ positive, or $(\mathrm{d})$ zero?

John Biddulph

Numerade Educator

Problem 11

(a) If a particle's position is given by $x=4 m-(12 \mathrm{~m} / \mathrm{s}) t+\left(3 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}$ (where $t$ is in seconds and $x$ is in meters), what is its velocity at $t_{1}=1$ s? (b) Is it moving in the positive or negative direction of $x$ just then? (c) What is its speed just then? (d) Is the speed larger or smaller at later times? (Try answering the next two questions without further calculation.) (c) Is there ever an instant when the velocity is zero? (f) Is there a time after $t_{3}=3 \mathrm{~s}$ when the particle is moving in the negative direction of $x ?$

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 12

The position of a particle moving along the $x$ axis is given in meters by $x=9.75 \mathrm{~m}+\left(1.5 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}$ where $t$ is in seconds. Calculate (a) the average velocity during the time interval $t=2.00 \mathrm{~s}$ to $t=3.00 \mathrm{~s} ;$ (b) the instantaneous velocity at $t=2.00 \mathrm{~s} ;(\mathrm{c})$ the instantaneous velocity at $t=3.00 \mathrm{~s} ;(\mathrm{d})$ the instantaneous velocity at $t=2.50 \mathrm{~s} ;$ and $(\mathrm{e})$ the instantaneous velocity when the particle is midway between its positions at $t=2.00 \mathrm{~s}$ and $t=3.00 \mathrm{~s}$ (f) Graph $x$ vs. $t$ and indicate your answers graphically.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 13

How far does the runner whose velocity-time graph is shown in Fig. $2-24$ travel in the time interval between
(a) $\mathrm{t}_{2}=2 \mathrm{~s}$ and $10 \mathrm{~s} ;(\mathrm{b})$
$\mathrm{t}_{12}=12 \mathrm{~s}$ and $\mathrm{t}_{16}=16 \mathrm{~s} ?$

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 14

Sketch a graph that is a possible description of position as a function of time for a particle that moves along the $x$ axis and, at $t=1 \mathrm{~s}$, has (a) zero velocity and positive acceleration;
(b) zero velocity and negative acceleration; (c) negative velocity and positive acceleration; (d) negative velocity and negative acceleration. (c) For which of these situations is the speed of the particle increasing at $t=1 \mathrm{~s} ?$

John Biddulph

Numerade Educator

Problem 15

What do the quantities (a) $(d x / d t)^{2}$ and (b) $d^{2} x / d t^{2}$ represent?
(c) What are their SI units?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 16

A frightened ostrich moves in a straight line with velocity described by the velocity-time graph of Fig. $2-25$. Sketch acceleration vs. time.

Alex Garger

Numerade Educator

Problem 17

A particle had a speed of $18 \mathrm{~m} / \mathrm{s}$ at a certain time, and $2.4 \mathrm{~s}$ later its speed was $30 \mathrm{~m} / \mathrm{s}$ in the opposite direction. What were the magnitude and direction of the average acceleration of the particle during this $2.4$ s interval?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 18

From $t_{0}=0$ to $t_{5}=5.00 \mathrm{~min}$, a man stands still, and from $t_{5}=5.00 \mathrm{~min}$ to $t_{10}=10.0 \mathrm{~min}$, he walks briskly in a straight line at a constant speed of $2.20 \mathrm{~m} / \mathrm{s}$. What are (a) his average velocity $\langle\vec{v}$ ) and (b) his average acceleration $\langle\vec{a})$ in the time interval $2.00 \mathrm{~min}$ to $8.00 \mathrm{~min} ?$ What are (c) $\langle\vec{v}\rangle$ and $\langle\vec{a}\rangle$ in the time interval $3.00 \mathrm{~min}$ to $9.00 \mathrm{~min} ?$ (d) Sketch $x$ vs. $t$ and $v$ vs. $t$, and indicate how the answers to (a) through (c) can be obtained from the graphs.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 19

The position of a particle moving along the $x$ axis depends on the time according to the equation $x=$ $c t^{2}-b t^{3}$, where $x$ is in meters and $t$ in seconds. (a) What units must $c$ and $b$ have? Let their numerical values be $3.0$ and $2.0 .$ respectively. (b) At what time does the particle reach its maximum positive $x$ position? From $t_{0}=0.0 \mathrm{~s}$ to $t_{4}=4.0 \mathrm{~s},(\mathrm{c})$ what distance does the particle move and (d) what is its displacement? At $t=1.0$, $2.0,3.0$, and $4.0 \mathrm{~s}$, what are (e) its velocities and (f) its accelerations?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 20

An automobile driver on a straight road increases the speed at a constant rate from $25 \mathrm{~km} / \mathrm{h}$ to $55 \mathrm{~km} / \mathrm{h}$ in $0.50 \mathrm{~min}$. A bicycle rider on a straight road speeds up at a constant rate from rest to $30 \mathrm{~km} / \mathrm{h}$ in $0.50 \mathrm{~min} .$ Calculate their accelerations.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 21

A muon (an elementary particle) moving in a straight line enters a region with a speed of $5.00 \times 10^{6} \mathrm{~m} / \mathrm{s}$ and then is slowed at the rate of $1.25 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2} .$ (a) How far does the muon take to stop? (b) Graph $x$ vs. $t$ and $v$ vs. $t$ for the muon.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 22

The head of a rattlesnake can accelerate at $50 \mathrm{~m} / \mathrm{s}^{2}$ in striking a victim. If a car could do as well, how long would it take to reach a speed of $100 \mathrm{~km} / \mathrm{h}$ from rest?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 23

An electron has a constant acceleration of $+3.2 \mathrm{~m} / \mathrm{s}^{2} \hat{\mathrm{i}}$. At a certain instant its velocity is $+9.6 \mathrm{~m} / \mathrm{s} \hat{\mathrm{i}}$. What is its velocity (a) $2.5 \mathrm{~s}$ earlier and (b) $2.5 \mathrm{~s}$ later?

Nishant Kumar

Numerade Educator

Problem 24

The speed of a bullet is measured to be $640 \mathrm{~m} / \mathrm{s}$ as the bullet emerges from a barrel of length $1.20 \mathrm{~m}$. Assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 25

Suppose a rocket ship in deep space moves with constant acceleration equal to $9.8 \mathrm{~m} / \mathrm{s}^{2}$, which gives the illusion of normal gravity during the flight. (a) If it starts from rest. how long will it take to acquire a speed one-tenth that of light, which travels at $3.0 \times 10^{8} \mathrm{~m} / \mathrm{s} ?$ (b) How far will it travel in so doing?

Averell Hause

Carnegie Mellon University

Problem 26

A jumbo jet must reach a speed of $360 \mathrm{~km} / \mathrm{h}$ on the runway for takeoff. What is the least constant acceleration needed for takeoff from a $1.80 \mathrm{~km}$ runway?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 27

An electron with initial velocity $v_{1}$ $=1.50 \times 10^{5} \mathrm{~m} / \mathrm{s}$ enters a region
$1.0 \mathrm{~cm}$ long where it is electrically accelerated (Fig. $2-26$ ). It emerges with velocity $v_{2}=5.70$ $\times 10^{6} \mathrm{~m} / \mathrm{s}$. What is its acceleration, assumed constant? (Such a process occurs in conventional television sets.)

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 28

A world's land speed record was set by Colonel John P. Stapp when in March 1954 he rode a rocket-propelled sled that moved along a track at $1020 \mathrm{~km} / \mathrm{h} . \mathrm{He}$ and the sled were brought to a stop in $1.4 \mathrm{~s}$. (See Fig. $2-13$ ) $\ln g$ units, what acceleration did he experience while stopping?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 29

The brakes on your automobile are capable of slowing down your car at a rate of $5.2 \mathrm{~m} / \mathrm{s}^{2} .(\mathrm{a})$ If you are going $137 \mathrm{~km} / \mathrm{h}$ and suddenly see a state trooper, what is the minimum time in which you can get your car under the $90 \mathrm{~km} / \mathrm{h}$ speed limit? The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.) (b) Graph $x$ vs. $t$ and $v \mathrm{vS}, t$ for such a deceleration.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 30

Figure $2-27$ depicts the motion of a particle moving along an $x$ axis with a constant acceleration. What are the magnitude and direction of the particle's acceleration?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 31

A car traveling $56.0$ $\mathrm{km} / \mathrm{h}$ is $24.0 \mathrm{~m}$ from a barrier when the driver slams on the brakes. The car hits the barrier $2.00 \mathrm{~s}$ later. (a) What is the car's constant acceleration before impact? (b) How fast is the car traveling at impact?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 32

A red train traveling at $72 \mathrm{~km} / \mathrm{h}$ and a green train traveling at $144 \mathrm{~km} / \mathrm{h}$ are headed toward one another along a straight, level track. When they are $950 \mathrm{~m}$ apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of $1.0 \mathrm{~m} / \mathrm{s}^{2}$. Is there a collision? If so, what is the speed of each train at impact? If not, what is the separation between the trains when they stop?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 33

A car moving with constant acceleration covered the distance between two points $60.0 \mathrm{~m}$ apart in $6.00 \mathrm{~s}$. Its speed as it passes the second point was $15.0 \mathrm{~m} / \mathrm{s} .(\mathrm{a}) \mathrm{What}$ was the speed at the first point? (b) What was the acceleration? (c) At what prior distance from the first point was the car at rest? (d) Graph $x$ vs. $t$ and $v$ vs. $t$ for the car from rest $\left(t_{1}=0 \mathrm{~s}\right)$.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 34

At the instant the traffic light turns green, an automobile starts with a constant acceleration $a$ of $2.2 \mathrm{~m} / \mathrm{s}^{2}$. At the same instant a truck, traveling with a constant speed of $9.5 \mathrm{~m} / \mathrm{s}$, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the car be traveling at that instant?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 35

To stop a car, first you require a certain reaction time to begin braking; then the car slows under the constant braking. Suppose that the total distance moved by your car during these two phases is $56.7 \mathrm{~m}$ when its initial speed is $80.5 \mathrm{~km} / \mathrm{h}$, and $24.4 \mathrm{~m}$ when its initial speed is $48.3 \mathrm{~km} / \mathrm{h}$. What are (a) your reaction time and (b) the magnitude of the braking acceleration?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 36

When a high-speed passenger train traveling at $161 \mathrm{~km} / \mathrm{h}$ rounds a bend, the engineer is shocked to see that a locomotive has improperly entered the track from a siding and is a distance $D=676 \mathrm{~m}$ ahead (Fig. $2-28)$. The locomotive is moving at $29.0 \mathrm{~km} / \mathrm{h}$. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant acceleration if a collision is to be just avoided? (b) Assume that the engineer is at $x=0$ when, at $t=0$, he first spots the locomotive. Sketch the $x(t)$ curves representing the locomotive and, high-speed train for the situations in which a collision is just avoided and is not quite avoided.

Manish Jain

Numerade Educator

Problem 37

An elevator cab in the New York Marquis Marriott has a total run of $190 \mathrm{~m}$. Its maximum speed is $305 \mathrm{~m} / \mathrm{min}$. Its acceleration (both speeding up and slowing) has a magnitude of $1.22 \mathrm{~m} / \mathrm{s}^{2} .$ (a) How far does the cab move while accelerating to full speed from rest? (b) How long does it take to make the nonstop $190 \mathrm{~m}$ run, starting and ending at rest?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 38

A shuffleboard disk is accelerated at a constant rate from rest to a speed of $6.0 \mathrm{~m} / \mathrm{s}$ over a $1.8 \mathrm{~m}$ distance by a player using a cue. At this point the disk loses contact with the cue and slows at a constant rate of $2.5 \mathrm{~m} / \mathrm{s}^{2}$ until it stops. (a) How much time elapses from when the disk begins to accelerate until it stops?
(b) What total distance does the disk travel?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 39

An electric vehicle starts from rest and accelerates at a rate of $2.0 \mathrm{~m} / \mathrm{s}^{2}$ in a straight line until it reaches a speed of $20 \mathrm{~m} / \mathrm{s}$. The vehicle then slows at a constant rate of $1.0 \mathrm{~m} / \mathrm{s}^{2}$ until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?

Donald Albin

Numerade Educator

Problem 40

In Fig. 2-29 a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an $x$ axis. At time $t_{1}=0 \mathrm{~s}$, the red car is at $x_{\mathrm{r}}=$ $0 \mathrm{~m}$ and the green car is at $x_{g}=220 \mathrm{~m}$. If the red car has a constant velocity of $20 \mathrm{~km} / \mathrm{h}$, the cars pass each other at $x=44.5 \mathrm{~m}$, and if it has a constant velocity of $40 \mathrm{~km} / \mathrm{h}$, they pass each other at $x=76.6$ $\mathrm{m}$. If the green car has a constant acceleration, what are (a) its initial velocity and (b) its acceleration?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 41

The position of a particle moving along an $x$ axis is given by $x=\left(12 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}-\left(2 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}$, where $x$ is in meters and $t$ is in seconds. (a) Determine the position, velocity, and acceleration of the particle at $t_{3}=3.0 \mathrm{~s}$. (b) What is the maximum positive coordinate reached by the particle and at what time is it reached? (c) What is the maximum positive velocity reached by the particle and at what time is it reached? (d) What is the acceleration of the particle at the instant the particle is not moving (other than at $\left.t_{0}=0\right)$ ? (e) Determine the average velocity of the particle between $t_{0}=0$ and $t_{3}=3 \mathrm{~s}$.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 42

An unrestrained child is playing on the front seat of a car that is traveling in a residential neighborhood at $35 \mathrm{~km} / \mathrm{h}$. (How many $\mathrm{mi} / \mathrm{h}$ is this? Is this car going too fast?) $\mathrm{A}$ small dog runs across the road and the driver applies the brakes, stopping the car quickly and missing the dog. Estimate the speed with which the child strikes the dashboard, presuming that the car stops before the child does so. Compare this speed with that of the world-record $100 \mathrm{~m}$ dash, which is run in about $10 \mathrm{~s}$.

DW

Duane Walton

Numerade Educator

Problem 43

Test results (Car \& Driver, February 1993, p. 48) on a Volkswagen Passat GLX show that when the brakes are fully applied it has an average braking acceleration of magnitude $8.9 \mathrm{~m} / \mathrm{s}^{2}$. If a preoccupied driver who is moving at a speed of 42 mph looks up suddenly and sees a stop light $30 \mathrm{~m}$ in front of $\mathrm{him}$, will he have sufficient time to stop? The weight of the Volkswagen is $3152 \mathrm{lb}$.

DW

Duane Walton

Numerade Educator

Problem 44

When we drive a car we usually describe our motion in terms of speed or velocity. A speed limit, such as $60 \mathrm{mi} / \mathrm{h}$, is a speed. When runners or joggers describe their motion, they often do so in terms of a pace - how long it takes to go a given distance. A 4-min mile (or better, "4 minutes/mile") is an example of a pace.
(a) Express the speed $60 \mathrm{mi} / \mathrm{h}$ as a pace in $\min / \mathrm{mi}$.
(b) I walk on my treadmill at a pace of $17 \mathrm{~min} / \mathrm{mi}$. What is $\mathrm{my}$ speed in $\mathrm{mi} / \mathrm{h}$ ?
(c) If I travel at a speed, $v$, given in $\mathrm{mi} / \mathrm{h}$, what is my pace, $p$, given in min/mi? (Write an equation that would permit casy conversion.)

DW

Duane Walton

Numerade Educator

Problem 45

The 9000 lb Spirit of America (designed to be the world's fastest car) accelerated from rest to a final velocity of 756 mph in a time of 45 s. What would the acceleration have been in meters per second? What distance would the driver, Craig Breedlove, have covered?

DW

Duane Walton

Numerade Educator

Problem 46

You and a friend decide to drive to New York from College Park, Maryland (near Washington, D.C.) on Saturday over the Thanksgiving break to go to a concert with some friends who live there. You figure you have to reach the vicinity of the city at 5 P.M. in order to meet your friends in time for dinner before the concert. It's about $220 \mathrm{mi}$ from the entrance to Route 95 to the vicinity of New York City. You would like to get on the highway about noon and stop for a bite to eat along the way. What does your average velocity have to be? If you keep an approximately constant speed (not a realistic assumption!), what should your speedometer read while you are driving?

DW

Duane Walton

Numerade Educator

Problem 47

You are working as a student intern for the National Aeronautics and Space Administration (NASA) and your supervisor wants you to perform an indirect calculation of the upward velocity of the space shuttle relative to the Earth's surface just $5.5 \mathrm{~s}$ after it is launched when it has an altitude of $100 \mathrm{~m}$. In order to obtain data, one of the engineers has wired a streamlined flare to the side of the shuttle that is gently released by remote control after $5.5 \mathrm{~s}$. If the flare hits the ground $8.5 \mathrm{~s}$ after it is released, what is the upward velocity of the flare (and hence of the shuttle) at the time of its release? (Neglect any effects of air resistance on the flare.)

DW

Duane Walton

Numerade Educator

Problem 48

You are arguing over a cell phone while trailing an unmarked police car by $25 \mathrm{~m} ;$ both your car and the police car are traveling at $110 \mathrm{~km} / \mathrm{h}$. Your argument diverts your attention from the police car for $2.0 \mathrm{~s}$ (long enough for you to look at the phonc and yell, "I won't do that!"). At the beginning of that $2.0 \mathrm{~s}$, the police officer begins emergency braking at $5.0 \mathrm{~m} / \mathrm{s}^{2} .(\mathrm{a})$ What is the separation between the two cars when your attention finally returns? Suppose that you take another $0.40 \mathrm{~s}$ to realize your danger and begin braking. (b) If you too brake at $5.0 \mathrm{~m} / \mathrm{s}^{2}$, what is your speed when you hit the police car?

Ma Ednelyn Lim

Numerade Educator

Problem 49

When a driver brings a car to a stop by braking as hard as possible, the stopping distance can be regarded as the sum of a "reaction distance," which is initial speed multiplied by the driver's reaction time, and a "braking distance," which is the distance traveled during braking. The following table gives typical values. (a) What reaction time is the driver assumed to have? (b) What is the car's stopping distance if the initial speed is $25 \mathrm{~m} / \mathrm{s} ?$

Alex Garger

Numerade Educator

Problem 50

In this problem we analyze the phenomenon of "tailgating" in a car on a highway at high speeds. This means traveling too close behind the car ahead of you. Tailgating leads to multiple car crashes when one of the cars in a line suddenly slows down. The question we want to answer is: "How close is too close?"
To answer this question, let's suppose you are driving on the highway at a speed of $100 \mathrm{~km} / \mathrm{h}$ (a bit more than $60 \mathrm{mi} / \mathrm{h}$ ). The driver ahead of you suddenly puts on his brakes. We need to calculate a number of things: how long it takes you to respond; how far you travel in that time, and how far the other car travels in that time.
(a) First let's estimate how long it takes you to respond. Two times are involved: how long it takes from the time you notice something happening till you start to move to the brake, and how long it takes to move your foot to the brake. You will need a ruler to do this. Take the ruler and have a friend hold it from the one end hanging straight down. Place your thumb and forefinger opposite the bottom of the ruler. As your friend releases the ruler suddenly, try to catch it with your thumb and forefinger. Measure how far it falls before you catch it. Do this three times and take the average distance Assuming the ruler is falling freely without air resistance (not a bad assumption), calculate how much time it takes you to catch it, $t_{1}$. Now estimate the time, $t_{2}$, it takes you to move your foot from the gas pedal to the brake pedal. Your reaction time is $t_{1}+t_{2}$.
(b) If you brake hard and fast, you can bring a typical car to rest from $100 \mathrm{~km} / \mathrm{h}$ (about $60 \mathrm{mi} / \mathrm{h}$ ) in 5 seconds.
1. Calculate your acceleration, $-a_{0}$, assuming that it is constant.
2. Suppose the driver ahead of you begins to brake with an acceleration $-a_{0}$. How far will he travel before he comes to a stop? (Hint: How much time will it take him to stop? What will be his average velocity over this time interval?)
(c) Now we can put these results together into a fairly realistic situation. You are driving on the highway at $100 \mathrm{~km} / \mathrm{hr}$ and there is a driver in front of you going at the same speed.
1. You see him start to slow immediately (an unreasonable but simplifying assumption). If you are also traveling $100 \mathrm{~km} / \mathrm{h}$, how far (in meters) do you travel before you begin to brake? If you can also produce the acceleration $-a_{0}$ when you brake, what will be the total distance you travel before you come to a stop?
2. If you don't notice the driver ahead of you beginning to brake for $1 \mathrm{~s}$, how much additional distance will you travel?
3. Discuss, on the basis of these calculations, what you think is a safe distance to stay behind a car at $60 \mathrm{mi} / \mathrm{h}$. Express your distance in "car lengths" (about $15 \mathrm{ft}$ ). Would you include a safety factor beyond what you have calculated here? How much?

Donald Albin

Numerade Educator

Problem 51

A motion detector that may be used in physics laboratories is shown in Fig. 2-30. It measures the distance to the nearest object by using a speaker and a microphone. The speaker clicks 30 times a second. The microphone detects the sound bouncing back from the nearest object in front of it. The computer calculates the time delay between making the sound and receiving the echo. It knows the speed of sound (about $343 \mathrm{~m} / \mathrm{s}$ at room temperature), and from that it can calculate the distance to the object from the time delay. (a) If the nearest object in front of the detector is too far away, the echo will not get back before a second click is emitted. Once that happens, the computer has no way of knowing that the echo isn't an echo from the second click and that the detector isn't giving correct results any more. How far away does the object have to be before that happens?
(b) The speed of sound changes a little bit with temperature. Let's try to get an idea of how important this is. At room temperature $\left(72{ }^{\circ} \mathrm{F}\right)$ the speed of sound is about $343 \mathrm{~m} / \mathrm{s}$. At $62{ }^{\circ} \mathrm{F}$ it is about $1 \%$ smaller. Suppose we are measuring an object that is really $1.5$ meters away at $72{ }^{\circ} \mathrm{F}$. What is the time delay $\Delta t$ that the computer detects before the echo returns? Now suppose the temperature is 62 ${ }^{\circ} \mathrm{F}$. If the computer detects a time delay of $\Delta t$ but (because it doesn't know the temperature) calculates the distance using the speed of sound appropriate for $72{ }^{\circ} \mathrm{F}$, how far away does the computer report the object to be?

Donald Albin

Numerade Educator

Problem 52

A bowling ball sits on a hard floor at a point that we take to be the origin. The ball is hit some number of times by a hammer. The ball moves along a line back and forth across the floor as a result of the hits. (See Fig. 2-31.) The region to the right of the origin is taken to be positive, but during its motion the ball is at times on both sides of the origin. After the ball has been moving for a while. a motion detector like the one discussed in Problem 51 is started and takes the following graph of the ball's velocity.
Answer the following questions with the symbols $L$ (left), $R$ (right), N (neither), or $\mathrm{C}$ (can't say which). Each question refers only to the time interval displayed by the computer.
(a) At which side of the origin is the ball for the time marked A?
(b) At the time marked $\mathrm{B}$, in which direction is the ball moving?
(c) Between the times $\mathrm{A}$ and $\mathrm{C}$, what is the direction of the ball's displacement?
(d) The ball receives a hit at the time marked D. In what direction is the ball moving after that hit?

DW

Duane Walton

Numerade Educator

Problem 53

In The Fellowship of the Ring, the hobbit Peregrine Took (Pippin for short) drops a rock into a well while the travelers are in the caves of Moria. This wakes a balrog (a bad thing) and causes all kinds of trouble. Pippin hears the rock hit the water $7.5 \mathrm{~s}$ after he drops it.
(a) Ignoring the time it takes the sound to get back up, how deep is the well?
(b) It is quite cool in the caves of Moria, and the speed of sound in air changes with temperature. Take the speed of sound to be 340 $\mathrm{m} / \mathrm{s}$ (it is pretty cool in that part of Moria). Was it $\mathrm{OK}$ to ignore the time it takes sound to get back up? Discuss and support your answer with a calculation.

Alex Garger

Numerade Educator

Problem 54

Passing in the Night" Figure $2-32$ represents the position vs. clock reading of the motion of two balls, $A$ and $B$,
moving on parallel tracks. Carefully sketch the figure on your homework paper and answer the following questions:
(a) Along the $t$ axis, mark with the symbol $t_{A}$ any instant or instants at which one ball is passing the other.
(b) Which ball is moving faster at clock reading $t_{B}$ ?
(c) Mark with the symbol $t_{C}$ any in- stant or instants at which the balls have the same velocity.
(d) Over the period of time shown in the diagram, which of the following is true of ball $B ?$ Explain your answer.
1. It is speeding up all the time.
2. It is slowing down all the time.
3. It is speeding up part of the time and slowing down part of the time.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 55

The graph in Fig. $2-33$ below shows the velocity graph of a cart moving on an air track. The track has a spring at one end and has its other end raised. The cart is started sliding up the track by pressing it against the spring and releasing it. The clock is started just as the cart leaves the spring. Take the direction the cart is moving in initially to be the positive $x$ direction and take the bottom of the spring to be the origin.
Letters point to $\mathrm{six}$ points on the velocity curve. For the physical situations described below, identify which of the letters corresponds to the situation described. You may use each letter more than once, more than one letter may be used for each answer, on none may be appropriate. If none is appropriate, use the letter $\mathbf{N}$.
(a) This point occurs when the cart is at its highest point on the track.
(b) At this point, the cart is instantaneously not moving.
(c) This is a point when the cart is in contact with the spring.
(d) At this point, the cart is moving down the track toward the origin.
(e) At this point, the cart has acceleration of zero.

DW

Duane Walton

Numerade Educator

Problem 56

A ball is launched up a ramp by a spring as shown in Fig. 2-34. At the time when the clock starts, the ball is near the bottom of the ramp and is rolling up the ramp as shown. It goes to the top and then rolls back down. For the graphs shown in Fig. 2-34, the horizontal axis represents the time. The vertical axis is unspecified. For each of the following quantities, select the letter of the graph that could provide a correct graph of the quantity for the ball in the situation shown (if the vertical axis were assigned the proper units). Use the $x$ and $y$ coordinates shown in the picture. If none of the graphs could work, write $\mathrm{N}$.
(a) The $x$ -component of the ball's position _________.
(b) The $y$ -component of the ball's velocity _________.
(c) The $x$ -component of the ball's acceleration _________.
(d) The $y$ -component of the normal force the ramp exerts on the ball _________.
(e) The $x$ -component of the ball's velocity _________.
(f) The $x$ -component of the force of gravity acting on the ball _________.

DW

Duane Walton

Numerade Educator

Problem 57

A model rocket, propelled by burning fuel, takes off vertically. Plot qualitatively (numbers not required) graphs of $y, v$, and $a$ versus $t$ for the rocket's flight. Indicate when the fuel is exhausted, when the rocket reaches maximum height, and when it returns to the ground.

Donald Albin

Numerade Educator

Problem 58

At time $t=$ 0, a rock climber accidentally allows a piton to fall freely from a high point on the rock wall to the valley below him. Then, after a short delay, his climbing partner, who is $10 \mathrm{~m}$ higher on the wall, throws a piton downward. The positions $y$ of the pitons versus $t$ during the fall are given in Fig. $2-35$. With what speed was the second piton thrown?

DW

Duane Walton

Numerade Educator

Problem 59

As two trains move along a track. their conductors suddenly notice that they are headed toward each other. Figure $2-36$ gives their velocities $v$ as functions of time $t$ as the conductors slow the trains. The slowing processes begin when the trains are $200 \mathrm{~m}$ apart. What is their separation when both trains have stopped?

DW

Duane Walton

Numerade Educator

Problem 60

As a runaway scientific balloon ascends at $19.6 \mathrm{~m} / \mathrm{s}$. one of its instrument packages breaks free of a harness and free-falls. Figure $2-37$ gives the vertical velocity of the package versus time, from before it breaks free to when it reaches the ground. (a) What maximum height above the break-free point does it rise? (b) How high was the break-free point above the ground?

Donald Albin

Numerade Educator

Problem 61

Two A particle moves along the $x$ axis with position function $x(t)$ as shown in Fig. 2
38. Make rough sketches of the particle's velocity versus time and its acceleration versus time for this motion.

DW

Duane Walton

Numerade Educator

Problem 62

Figure 2-39 gives the velocity $v(\mathrm{~m} / \mathrm{s})$ versus time $t(\mathrm{~s})$ for a particle moving along an $x$ axis. The area between the time axis and the plotted curve is given for the two portions of the graph. At $t=t_{A}$ (at one of the crossing points in the plotted fig. ure), the particle's position is $x=14$
$\mathrm{m}$. What is its position at
(a) $t=0$ and
(b) $t=t_{B}$ ?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 63

This assignment is based on the Physics Pholk Song CD distributed by Pasco scientific. The words to these songs are also available through the Dickinson College Web site at http://physics.dickinson.edu.
(a) Refer to the motion described in the first verse of the Motion Detector Rag; namely, you are moving for the same amount of time that you are standing. Sketch a position vs. time graph for this motion. Also, describe the shape of the graph in words.
(b) Refer to the motion described in the second verse of the $\mathrm{Mo}$ tion Detector Rag. In this verse, you are making a "steep downslope," then a "gentle up-slope," and last a flat line. You spend the same amount of time engaged in each of these actions. Sketch a position vs. time graph of this motion. Also, describe what you are doing in words. That is, are you standing still, moving away from the origin (or motion detector), moving toward the origin (or motion detector)? Which motion is the most rapid, and so on?
(c) Refer to the motion described in the third verse of the Motion Detector Rag. You start from rest and move away from the motion detector at an acceleration of $+1.0 \mathrm{~m} / \mathrm{s}^{2}$ for 5 seconds. Sketch the acceleration vs. time graph to this motion. Sketch the corresponding velocity vs. time graph. Sketch the shape of the corresponding position vs, time graph.

Manish Jain

Numerade Educator

Problem 64

At time $t=0$, a hockey puck is sent sliding over a frozen lake, directly into a strong wind. Figure $2-40$ gives the velocity $v$ of the puck vs. time, as the puck moves along a single axis. At $t=14 \mathrm{~s}$, what is its position relative to its position at $t=0 ?$

Nicholas Mogoi

Numerade Educator

Problem 65

In each of the following situations you will be asked to refer to the mathematical definitions and the concepts associated with the number line. Note that being more positive is the same as being less negative, and so on.
(a) Suppose an object undergoes a change in velocity from $+1 \mathrm{~m} / \mathrm{s}$ to $+4 \mathrm{~m} / \mathrm{s}$. Is its velocity becoming more positive or less positive? What is meant by more positive? Less positive? Is the acceleration positive or negative?
(b) Suppose an object undergoes a change in velocity from $-4 \mathrm{~m} / \mathrm{s}$ to $-1 \mathrm{~m} / \mathrm{s}$. Is its velocity becoming more positive or less positive? What is meant by more positive? Less positive? Is the acceleration positive or negative?
(c) Suppose an object is turning around so that it undergoes a change in velocity from $-2 \mathrm{~m} / \mathrm{s}$ to $+2 \mathrm{~m} / \mathrm{s}$. Is its velocity becoming more positive or less positive than it was before? What is meant by more positive? Less positive? Is it undergoing an acceleration while it is turning around? Is the acceleration positive or negative?
(d) Another object is turning around so that it undergoes a change in velocity from $+1 \mathrm{~m} / \mathrm{s}$ to $-1 \mathrm{~m} / \mathrm{s}$. Is its velocity becoming more positive or less positive than it was before? What is meant by more positive? Less positive? Is it undergoing an acceleration while it is turning around? Is the acceleration positive or negative?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 66

Graph A bowling ball was set into motion on a fairly smooth level surface, and data were collected for the total distance covered by the ball at each of four times. These data are shown in the table.
(a) Plot the data points on a graph.
(b) Use a ruler to draw a straight line that passes as close as possible to the data points you have graphed.
(c) Using methods you were taught in algebra, calculate the value of the slope, $m$, and find the value of the intercept, $b$, of the line you have sketched through the data.

Manish Jain

Numerade Educator

Problem 67

A bowling ball is set into motion on a smooth level surface, and data were collected for the total distance covered by the ball at each of four times. These data are shown in the table in Problem 66 . Your job is to learn to use a spreadsheet program $-$ for example, Microsoft Excel-to create a mathematical model of the bowling ball motion data shown. You are to find what you think is the best value for the slope, $m$, and the $y$ -intercept, $b$. Practicing with a tutorial worksheet entitled MODTUT.XLS will help you to learn about the process of modeling for a linear relationship. Ask your instructor where to find this tutorial worksheet.

After using the tutorial, you can create a model for the bowling ball data given above. To do this:
(a) Open a new worksheet and enter a title for your bowling ball graph.
(b) Set the $y$ -label to Distance $(m)$ and the $x$ -label to Time $(s)$.
(c) Refer to the data table above. Enter the measured times for the bowling ball in the Time $(s)$ column (formerly $x$ -label).
(d) Set the $y$ -exp column to $D$ -data $(m)$ and enter the measured distances for the bowling ball (probably something like $0.00 \mathrm{~m}, 2.00$ $\mathrm{m}, 4.00 \mathrm{~m}$, and $6.00 \mathrm{~m} .$ ).
(e) Place the symbol $m$ (for slope) in the cell B1. Place the symbol $b$ (for $y$ -intercept) in cell $\mathrm{B}$ 2.
(f) Set the $y$ -theory column to D-model $(\mathrm{m})$ and then put the appropriate equation for a straight line of the form Distance = $\mathrm{m}^{*}$ Time $+\mathrm{b}$ in cells $\mathrm{C} 7$ through $\mathrm{C} 12$. Be sure to refer to cells $\mathrm{Cl}$ for slope and $C 2$ for $y$ -intercept as absolutes; that is, use $\$ C \$ 1$ and $\$ C \$ 2$ when referring to them.
(g) Use the spreadsheet graphing feature to create a graph of the data in the D-exp and D-theory columns as a function of the data in the Time column.
(h) Change the values in cells $\mathrm{Cl}$ and $\mathrm{C} 2$ until your theoretical line matches as closely as possible your red experimental data points in the graph window.
(i) Discuss the meaning of the slope of a graph of distance vs. time. What does it tell you about the motion of the bowling ball?

Manish Jain

Numerade Educator

Problem 68

After doing a number of the exercises with carts and fans on ramps, it is easy to draw the conclusion that everything that moves is moving at cither a constant velocity or a constant acceleration. Let's cxamine the horizontal motion of a triangular frame with a pendulum at its center that has been given a push. It undergoes an unusual motion. You should determine whether or not it is moving at either a constant velocity or constant acceleration. (Note: You may want to look at the motion of the triangular frame by viewing the digital movie entitled PASCO070. This movie is included on the VideoPoint compact disk. If you are not using VideoPoint, your instructor may make the movie available to you some other way.)
The images in Fig. $2-41$ are taken from the 7 th, 16 th, and 25 th frames of that movie.
Data for the position of the center of the horizontal bar of the triangle were taken every tenth of a second during its first second of motion. The origin was placed at the zero centimeter mark of a fixed meter stick. These data are in the table below.
(a) Examine the position vs. time graph of the data shown above. Does the triangle appear to have a constant velocity throughout the first second? A constant acceleration? Why or why not?
(b) Discuss the nature of the motion based on the shape of the graph. At approximately what time, if any, is the triangle changing direction? At approximately what time does it have the greatest negative velocity? The greatest positive velocity? Explain the reasons for your answers.
(c) Use the data table and the definition of average velocity to calculate the average velocity of the triangle at each of the times between $0.100 \mathrm{~s}$ and $0.900 \mathrm{~s}$. In this case you should use the position just before the indicated time and the position just after the indicated time in your calculation. For example, to calculate the average velocity at $t_{2}=0.100$ seconds, use $x_{3}=44.5 \mathrm{~cm}$ and $x_{1}=52.1$ $\mathrm{cm}$ along with the differences of the times at $t_{3}$ and $t_{1} .$ Hint: Use only times and positions in the gray boxes to get a velocity in a gray box and use only times and positions in the white boxes to get a velocity in a white box.
(d) Since people usually refer to velocity as distance divided by time. maybe we can calculate the average velocities as simply $x_{1} / t_{1}, x_{2} / l_{2}$, $x_{y} / l_{3}$, and so on. This would be easier. Is this an equivalent method for finding the velocities at the different times? Try using this method of calculation if you are not sure. Give reasons for your answer.
(e) Often, when an oddly shaped but smooth graph is obtained from data it is possible to fit a polynomial to it. For example, a fourth-order polynomial that fits the data is
$$\left.x=\mid\left(-376 \mathrm{~cm} / \mathrm{s}^{4}\right) t^{4}+\left(719 \mathrm{~cm} / \mathrm{s}^{3}\right) t^{3}-\left(347 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}+(5.63 \mathrm{~cm} / \mathrm{s}) t+52.1 \mathrm{~cm}\right\}$$
Using this polynomial approximation, find the instantaneous velocity at $t=0.700 \mathrm{~s}$. Comment on how your answer compares to the average velocity you calculated at $0.700 \mathrm{~s}$. Are the two values close? Is that what you expect?

Donald Albin

Numerade Educator

Problem 69

At the Cedar Point Amusement Park in Ohio, a cage containing people is moving at a high initial velocity as the result of a previous free fall. It changes direction on a curved track and then coasts in a horizontal direction until the brakes are applied. This situation is depicted in a digital movie entitled DSON002. (Note: This movie is included on the VideoPoint compact disk. If you are not using VideoPoint, your instructor may make the movie available to you some other way.)
(a) Use video analysis software to gather data for the horizontal positions of the tail of the cage in meters as a function of time. Don't forget to use the scale on the title screen of the movie so your results are in meters rather than pixels. Summarize this data in a table or in a printout attached to your homework.
(b) Transfer your data to a spreadsheet and do a parabolic model to show that within $5 \%$ or better $x=\left(-7.5 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}+(22.5 \mathrm{~m} / \mathrm{s}) t+$
$2.38 \mathrm{~m}$. Please attach a printout of this model and graph with your name on it to your submission as "proof of completion."(Note: Your judgments about the location of the cage tail may lead to slightly different results.)
(c) Use the equation you found along with its interpretation as embodied in the first kinematic equation to determine the horizontal acceleration, $a$, of the cage as it slows down. What is its initial horizontal velocity, $v_{1}$, at time $t=0 \mathrm{~s}$ ? What is the initial position, $x_{1}$, of the cage?
(d) The movie ends before the cage comes to a complete stop. Use your knowledge of $a, v_{1}$, and $x_{1}$ along with kinematic equations to determine the horizontal position of the cage when it comes to a complete stop so that the final velocity of the cage is given by $v_{2}=$ $v=0.00 \mathrm{~m} / \mathrm{s}$

Manish Jain

Numerade Educator

Problem 70

Three digital movies depicting the motions of four single objects have been selected for you to examine using a video-analysis program. They are as follows:
PASCO004: A cart moves on an upper track while another moves on a track just below.
PASCO153: A metal ball attached to a string swings gently. HRSY003: A boat with people moves in a water trough at Hershey Amusement Park.
Please examine the horizontal motion of each object carefully by viewing the digital movies. In other words, just examine the motion in the $x$ direction (and ignore any slight motions in the $y$ direction). You may use LoggerPro 3, VideoPoint, VideoGraph, or World-inMotion digital analysis software and a spreadsheet to analyze the motion in more detail if needed. Based on what you have learned so far, there is more than one analysis method that can be used to answer the questions that follow. Note: Since we are interested only in the nature of these motions (not exact values) you do not need to scale any of the movies. Working in pixel units is fine.
(a) Which of these four objects (upper cart, lower cart, metal ball, or boat), if any, move at a constant horizontal velocity? Cite the evidence for your conclusions.
(b) Which of these four objects, if any, move at a constant horizontal acceleration? Cite the evidence for your conclusions.
(c) Which of these four objects, if any, move at neither a constant horizontal velocity nor acceleration? Cite the evidence for your conclusions.
(d) The kinematic equations are very useful for describing motions. Which of the four motions, if any, cannot be described using the kinematic equations? Explain the reasons for your answer.

Manish Jain

Numerade Educator

Problem 71

Figure $2-42$ shows the velocity vs. time graph for an object constrained to move in one dimension. The positive direction is to the right.
(a) At what times, or during what time periods, is the object speeding up?
(b) At what times, or during what time periods, is the object slowing down?
(c) At what times, or during what time periods, does the object have a constant velocity?
(d) At what times, or during what time periods, is the object at rest?
If there is no time or time period for which a given condition exists, state that explicitly.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 72

Figure $2-42$ shows the velocity vs. time graph for an object constrained to move along a line. The positive direction is to the right.
(a) At what times, or during what time periods, is the object speeding up and moving to the right?
(b) At what times, or during what time periods, is the object slowing down and moving to the right?
(c) At what times, or during what time periods, does the object have a constant velocity to the right?
(d) At what times, or during what time periods, is the object speeding up and moving to the left?
(e) At what times, or during what time periods, is the object slowing down and moving to the left?
(f) At what times, or during what time periods, does the object have a constant velocity to the left?
If there is no time or time period for which a given condition exists, state that explicitly.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 73

Figure $2-42$ shows the velocity vs. time graph for an object constrained to move along a line. The positive direction is to the right.
(a) At what times, or during what time periods, is the object's acceleration zero?
(b) At what times, or during what time periods, is the object's acceleration constant?
(c) At what times, or during what time periods, is the object's acceleration changing? If there is no time or time period for which a given condition exists, state that explicitly.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 74

Figure $2-42$ shows the velocity vs. time graph for an object constrained to move along a line. The positive direction is to the right.
(a) At what times, or during what time periods, is the object's acceleration increasing and directed to the right?
(b) At what times, or during what time periods, is the object's acceleration decreasing and directed to the right?
(c) At what times, or during what time periods, does the object have a constant acceleration to the right?
(d) At what times, or during what time periods, is the object's acceleration increasing and directed to the left?
(e) At what times, or during what time periods, is the object's acceleration decreasing and directed to the left?
(d) At what times, or during what time periods, does the object have a constant acceleration to the left?
If there is no time or time period for which a given condition exists, state that explicitly.

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator