Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 2

Motion in One Dimension - all with Video Answers

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Chapter Questions

Problem 1

On the graph below, what is the total distance traveled during the recorded time interval? What is the displacement?

Z S

Z S

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Problem 2

On a position-time graph such as the one above, what represents the instantaneous velocity?

Z S

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Problem 3

The position-time graph for a bug crawling along a line is shown in item 4 below. Determine whether the velocity is positive, negative, or zero at each of the times marked on the graph.

Prabhat Tyagi

Numerade Educator

Problem 4

Use the position-time graph below to answer the following questions:
a. During which time interval(s) is the velocity negative?
b. During which time interval(s) is the velocity positive?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 5

If the average velocity of a duck is zero in a given time interval, what can you say about the displacement of the duck for that interval?

Z S

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Problem 6

Velocity can be either positive or negative, depending on the direction of the displacement. The time interval, $\Delta t$, is always positive. Why?

Surjit Tewari

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Problem 7

See Sample Problem A. A school bus takes $0.530 \mathrm{h}$ to reach the school from your house. If the average velocity of the bus is $19.0 \mathrm{km} / \mathrm{h}$ to the east, what is the displacement?

Surjit Tewari

Numerade Educator

Problem 8

See Sample Problem A. The Olympic record for the marathon is $2.00 \mathrm{h}$ $9.00 \mathrm{min}, 21.0 \mathrm{s} .$ If the average speed of a runner achieving this record is $5.436 \mathrm{m} / \mathrm{s},$ what is the marathon distance?

Surjit Tewari

Numerade Educator

Problem 9

See Sample Problem A. Two cars are traveling on a desert road, as shown below. After $5.0 \mathrm{s}$, they are side by side at the next telephone pole. The distance between the poles is
$70.0 \mathrm{m} .$ Identify the following quantities:
a. the displacement of car A after $5.0 \mathrm{s}$
b. the displacement of car $\mathrm{B}$ after $5.0 \mathrm{s}$
c. the average velocity of car A during $5.0 \mathrm{s}$
d. the average velocity of car $\mathrm{B}$ during $5.0 \mathrm{s}$

Paul A.

California State Polytechnic University, Pomona

Problem 10

Sally travels by car from one city to another. She drives for 30.0 min at $80.0 \mathrm{km} / \mathrm{h}, 12.0 \mathrm{min}$ at
$105 \mathrm{km} / \mathrm{h},$ and $45.0 \mathrm{min}$ at $40.0 \mathrm{km} / \mathrm{h},$ and she
spends 15.0 min eating lunch and buying gas.
a. Determine the average speed for the trip.
b. Determine the total distance traveled.

Surjit Tewari

Numerade Educator

Problem 11

Runner $A$ is initially $6.0 \mathrm{km}$ west of a flagpole and is running with a constant velocity of $9.0 \mathrm{km} / \mathrm{h}$ due east. Runner $\mathrm{B}$ is initially $5.0 \mathrm{km}$ east of the flagpole and is running with a constant velocity of $8.0 \mathrm{km} / \mathrm{h}$ due west. What will be the distance of the two runners from the flagpole when their paths cross? (It is not necessary to convert your answer from kilometers to meters for this problem. You may leave it in kilometers.)

Surjit Tewari

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Problem 12

What would be the acceleration of a turtle that is moving with a constant velocity of $0.25 \mathrm{m} / \mathrm{s}$ to the right?

Z S

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Problem 13

Sketch the velocity-time graphs for the following motions.
a. a city bus that is moving with a constant velocity
b. a wheelbarrow that is speeding up at a uniform rate of acceleration while moving in the positive direction
c. a tiger that is speeding up at a uniform rate of acceleration while moving in the negative direction
d. an iguana that is slowing down at a uniform rate of acceleration while moving in the positive direction
e. a camel that is slowing down at a uniform rate of acceleration while moving in the negative direction

Surjit Tewari

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Problem 14

If a car is traveling eastward, can its acceleration be westward? Explain your answer, and use an example in your explanation.

Surjit Tewari

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Problem 15

The strobe photographs below show a disk moving from left to right under different conditions. The time interval between images is constant. Assuming that the direction to the right is positive, identify the following types of motion in each photograph. (Some may have more than one type of motion.)
a. the acceleration is positive
b. the acceleration is negative
c. the velocity is constant

Prashant Bana

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Problem 16

See Sample Problem $\boldsymbol{B}$ A car traveling in a straight line has a velocity of $+5.0 \mathrm{m} / \mathrm{s} .$ After an acceleration of $0.75 \mathrm{m} / \mathrm{s}^{2},$ the car's velocity is $+8.0 \mathrm{m} / \mathrm{s}$. In what time interval did the acceleration occur?

Surjit Tewari

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Problem 17

see Sample Problem $\boldsymbol{B}$ The velocity-time graph for an object moving along a straight path is shown below. Find the average accelerations during the time intervals $0.0 \mathrm{s}$ to $5.0 \mathrm{s}$ $5.0 \mathrm{s}$ to $15.0 \mathrm{s},$ and $0.0 \mathrm{s}$ to $20.0 \mathrm{s}$ CANT COPY THE FIGURE

Surjit Tewari

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Problem 18

A bus slows down uniformly from $75.0 \mathrm{km} / \mathrm{h}$ $(21 \mathrm{m} / \mathrm{s})$ to $0 \mathrm{km} / \mathrm{h}$ in $21 \mathrm{s}$. How far does it travel before stopping?

Surjit Tewari

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Problem 19

A car accelerates uniformly from rest to a speed of $65 \mathrm{km} / \mathrm{h}(18 \mathrm{m} / \mathrm{s})$ in $12 \mathrm{s} .$ Find the distance the car travels during this time.

Surjit Tewari

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Problem 20

see Sample Problem $D$ A car traveling at $+7.0 \mathrm{m} / \mathrm{s}$ accelerates at the rate of $+0.80 \mathrm{m} / \mathrm{s}^{2}$ for an interval of $2.0 \mathrm{s}$. Find $v_{f}$

Surjit Tewari

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Problem 21

see Sample Problem $D$ A car accelerates from rest at $-3.00 \mathrm{m} / \mathrm{s}^{2}$
a. What is the velocity at the end of 5.0 s?
b. What is the displacement after 5.0 s?

Surjit Tewari

Numerade Educator

Problem 22

see Sample Problem $D$ A car starts from rest and travels for 5.0 s with a uniform acceleration of $+1.5 \mathrm{m} / \mathrm{s}^{2} .$ The driver then applies the brakes, causing a uniform acceleration of $-2.0 \mathrm{m} / \mathrm{s}^{2} .$ If the brakes are applied for $3.0 \mathrm{s}$, how fast is the car going at the end of the braking period, and how far has it gone from its start?

Surjit Tewari

Numerade Educator

Problem 23

see Sample Problem $D$ A boy sledding down a hill accelerates at $1.40 \mathrm{m} / \mathrm{s}^{2} .$ If he started from rest, in what distance would he reach a speed of $7.00 \mathrm{m} / \mathrm{s} ?$

Surjit Tewari

Numerade Educator

Problem 24

see Sample Problem $E$ A sailboat starts from rest and accelerates at a rate of
$0.21 \mathrm{m} / \mathrm{s}^{2}$ over a distance of $280 \mathrm{m}$
a. Find the magnitude of the boat's final velocity.
b. Find the time it takes the boat to travel this distance.

Surjit Tewari

Numerade Educator

Problem 25

see Sample Problem $D$ An elevator is moving upward at $1.20 \mathrm{m} / \mathrm{s}$ when it experiences an acceleration of $0.31 \mathrm{m} / \mathrm{s}^{2}$ downward, over a distance of $0.75 \mathrm{m}$. What will its final velocity be?

Surjit Tewari

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Problem 26

A ball is thrown vertically upward.
a. What happens to the ball's velocity while the ball is in the air?
b. What is its velocity when it reaches its maximum altitude?
c. What is its acceleration when it reaches its maximum altitude?
d. What is its acceleration just before it hits the ground?
e. Does its acceleration increase, decrease, or remain constant?

Surjit Tewari

Numerade Educator

Problem 27

The image at right is a strobe photograph of two falling balls released simultancously. (This motion does not take place in a vacuum.) The ball on the left side is solid, and the ball on the right side is a hollow table-tennis ball. Analyze the motion of both balls in terms of
velocity and acceleration.

Surjit Tewari

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Problem 28

A juggler throws a bowling pin into the air with an initial velocity $v_{i}$. Another juggler drops a pin at the same instant. Compare the accelerations of the two pins while they are in the air.

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Problem 29

A bouquet is thrown upward.
a. Will the value for the bouquet's displacement be the same no matter where you place the origin of the coordinate system?
b. Will the value for the bouquet's velocity be the same?
c. Will the value for the bouquet's acceleration be the same?

Surjit Tewari

Numerade Educator

Problem 30

See Sample Problem $F$ A worker drops a wrench from the top of a tower $80.0 \mathrm{m}$ tall. What is the velocity when the wrench strikes the ground?

Surjit Tewari

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Problem 31

See Sample Problem $F$ A peregrine falcon dives at a pigeon. The falcon starts downward from rest with free-fall acceleration. If the pigeon is $76.0 \mathrm{m}$ below the initial position of the falcon, how long does the falcon take to reach the pigeon? Assume that the pigeon remains at rest.

Surjit Tewari

Numerade Educator

Problem 32

See Sample Problem $F$ A ball is thrown upward from the ground with an initial speed of $25 \mathrm{m} / \mathrm{s} ;$ at the same instant, a ball is dropped from rest from a building 15 m high. After how long will the balls be at the same height?

Surjit Tewari

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Problem 33

If the average speed of an orbiting space shuttle is $27800 \mathrm{km} / \mathrm{h},$ determine the time required for it to circle Earth. Assume that the shuttle is orbiting about $320.0 \mathrm{km}$ above Earth's surface, and that Earth's radius is $6380 \mathrm{km}$

Vishal Gupta

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Problem 34

A ball is thrown directly upward into the air. The graph below shows the vertical position of the ball with respect to time.
Aow much time does the ball take to reach its maximum height? b. How much time does the ball take to reach one-half its maximum height? c. Estimate the slope of $\Delta y / \Delta t$ at $t=0.05 \mathrm{s}, t=$ $0.10 \mathrm{s}, t=0.15 \mathrm{s},$ and $t=0.20 \mathrm{s} .$ On your paper, draw a coordinate system with velocity ( $v$ ) on the $y$ -axis and time ( $t$ ) on the $x$ -axis. Plot your velocity estimates against time. d. From your graph, determine what the acceleration on the ball is.

Laszlo Zalavari

Laszlo Zalavari

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Problem 35

A train travels between stations 1 and $2,$ as shown below. The engineer of the train is instructed to start from rest at station 1 and accelerate uniformly between points $A$ and $B$, then coast with a uniform velocity between points $B$ and $C$, and finally accelerate uniformly between points $C$ and $D$ until the train stops at station $2 .$ The distances $A B, B C$, and $C D$ are all equal, and it takes 5.00 min to travel between the two stations. Assume that the uniform accelerations have the same
magnitude, even when they are opposite in direction.
a. How much of this 5.00 min period does the train spend between points $A$ and $B ?$
b. How much of this 5.00 min period does the train spend between points $B$ and $C ?$
c. How much of this 5.00 min period does the train spend between points $C$ and $D ?$

Sachin Rao

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Problem 36

Two students are on a balcony $19.6 \mathrm{m}$ above the street. One student throws a ball vertically downward at $14.7 \mathrm{m} / \mathrm{s} .$ At the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down.
a. What is the difference in the time the balls spend in the air?
b. What is the velocity of each ball as it strikes the ground?
c. How far apart are the balls $0.800 \mathrm{s}$ after they are thrown?

Surjit Tewari

Numerade Educator

Problem 37

A rocket moves upward, starting from rest with an acceleration of $+29.4 \mathrm{m} / \mathrm{s}^{2}$ for $3.98 \mathrm{s}$. It runs out of fuel at the end of the 3.98 s but does not stop. How high does it rise above the ground?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

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Problem 38

Two cars travel westward along a straight highway, one at a constant velocity of $85 \mathrm{km} / \mathrm{h},$ and the other
at a constant velocity of $115 \mathrm{km} / \mathrm{h}$
a. Assuming that both cars start at the same point, how much sooner does the faster car arrive at a destination $16 \mathrm{km}$ away?
b. How far must the cars travel for the faster car
to arrive 15 min before the slower car?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 39

A small first-aid kit is dropped by a rock climber who is descending steadily at $1.3 \mathrm{m} / \mathrm{s}$. After $2.5 \mathrm{s}$ what is the velocity of the first-aid kit, and how far is the kit below the climber?

Surjit Tewari

Numerade Educator

Problem 40

A small fish is dropped by a pelican that is rising steadily at $0.50 \mathrm{m} / \mathrm{s}$
a. After $2.5 \mathrm{s},$ what is the velocity of the fish?
b. How far below the pelican is the fish after 2.5 s?

Surjit Tewari

Numerade Educator

Problem 41

A ranger in a national park is driving at $56 \mathrm{km} / \mathrm{h}$ when a decr jumps onto the road $65 \mathrm{m}$ ahead of the vehicle. After a reaction time of $t$ s, the ranger applies the brakes to produce an acceleration of $-3.0 \mathrm{m} / \mathrm{s}^{2} .$ What is the maximum reaction time allowed if the ranger is to avoid hitting the deer?

Surjit Tewari

Numerade Educator

Problem 42

A speeder passes a parked police car at $30.0 \mathrm{m} / \mathrm{s}$ The police car starts from rest with a uniform acceleration of $2.44 \mathrm{m} / \mathrm{s}^{2}$
a. How much time passes before the speeder is overtaken by the police car?
b. How far does the speeder get before being overtaken by the police car?

Manish Kumar ( Iit K )

Manish Kumar ( Iit K )

Numerade Educator

Problem 43

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at $+13.0 \mathrm{m} / \mathrm{s}^{2}$ At $t_{1}$ the rocket engine is shut down and the sled moves with constant velocity $\nu$ until $t_{2}$. The total distance traveled by the sled is $5.30 \times 10^{3} \mathrm{m}$ and the total time is $90.0 \mathrm{s}$. Find $t_{l}, t_{2},$ and $v$ (See Appendix A for hints on solving quadratic equations.)

Surjit Tewari

Numerade Educator

Problem 44

At the 5800 m mark, the sled in the previous question begins to accelerate at $-7.0 \mathrm{m} / \mathrm{s}^{2} .$ Use your answers from item 43 to answer the following questions.
a. What is the final position of the sled when it comes to rest?
b. How long does it take for the sled to come to rest?

Surjit Tewari

Numerade Educator

Problem 45

A tennis ball with a velocity of $+10.0 \mathrm{m} / \mathrm{s}$ to the right is thrown perpendicularly at a wall. After striking the wall, the ball rebounds in the opposite direction with a velocity of $-8.0 \mathrm{m} / \mathrm{s}$ to the left. If the ball is in contact with the wall for $0.012 \mathrm{s}$, what is the average acceleration of the ball while it is in contact with the wall?

Surjit Tewari

Numerade Educator

Problem 46

A parachutist descending at a speed of $10.0 \mathrm{m} / \mathrm{s}$ loses a shoe at an altitude of $50.0 \mathrm{m}$
a. When does the shoe reach the ground?
b. What is the velocity of the shoe just before it hits the ground?

Surjit Tewari

Numerade Educator

Problem 47

A mountain climber stands at the top of a 50.0 m cliff hanging over a calm pool of water. The climber throws two stones vertically $1.0 \mathrm{s}$ apart and observes that they cause a single splash when they hit the water. The first stone has an initial velocity of $+2.0 \mathrm{m} / \mathrm{s}$
a. How long after release of the first stone will the two stones hit the water?
b. What is the initial velocity of the second stone when it is thrown?
c. What will the velocity of each stone be at the instant both stones hit the water?

Dominador Tan

Numerade Educator

Problem 48

A model rocket is launched straight upward with an initial speed of $50.0 \mathrm{m} / \mathrm{s} .$ It accelerates with a constant upward acceleration of $2.00 \mathrm{m} / \mathrm{s}^{2}$ until its engines stop at an altitude of $150 \mathrm{m}$
What is the maximum height reached by the rocket?
b. When does the rocket reach maximum height?
c. How long is the rocket in the air?

Surjit Tewari

Numerade Educator

Problem 49

A professional race-car driver buys a car that can accelerate at $+5.9 \mathrm{m} / \mathrm{s}^{2} .$ The racer decides to race against another driver in a souped-up stock car. Both start from rest, but the stock-car driver leaves
$1.0 \mathrm{s}$ before the driver of the race car. The stock car moves with a constant acceleration of $+3.6 \mathrm{m} / \mathrm{s}^{2}$
a. Find the time it takes the race-car driver to overtake the stock-car driver.
b. Find the distance the two drivers travel before they are side by side.
c. Find the velocities of both cars at the instant they are side by side.

Surjit Tewari

Numerade Educator

Problem 50

Two cars are traveling along a straight line in the same direction, the lead car at $25 \mathrm{m} / \mathrm{s}$ and the other car at $35 \mathrm{m} / \mathrm{s}$. At the moment the cars are $45 \mathrm{m}$ apart, the lead driver applies the brakes, causing the car to have an acceleration of $-2.0 \mathrm{m} / \mathrm{s}^{2}$
a. How long does it take for the lead car to stop?
b. Assume that the driver of the chasing car applies the brakes at the same time as the driver of the lead car. What must the chasing car's minimum negative acceleration be to avoid hitting the lead car?
c. How long does it take the chasing car to stop?

Surjit Tewari

Numerade Educator

Problem 51

One swimmer in a relay race has a 0.50 s lead and is swimming at a constant speed of $4.00 \mathrm{m} / \mathrm{s}$. The swimmer has $20.0 \mathrm{m}$ to swim before reaching the end of the pool. A second swimmer moves in the same direction as the leader. What constant speed must the second swimmer have in order to catch up to the leader at the end of the pool?

Guilherme Barros

Guilherme Barros

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