Essential College Physics

Andrew F. Rex, Richard Wolfson

Chapter 2

Motion in One Dimension - all with Video Answers

Educators

+ 5 more educators

Chapter Questions

Problem 1

In one-dimensional motion, when are displacement and distance traveled the same? When are they different?

Nishant Kumar

Nishant Kumar

Numerade Educator

Problem 2

In one-dimensional motion, when are average speed and average velocity the same? When are they different?

Luis Rios

Numerade Educator

Problem 3

If the acceleration of an object is zero, can its velocity be negative?

Luis Rios

Numerade Educator

Problem 4

If the acceleration of an object is negative, can its velocity be zero? Can its velocity be positive? Explain.

Luis Rios

Numerade Educator

Problem 5

Can an object have zero velocity yet nonzero acceleration? Give an example.

Luis Rios

Numerade Educator

Problem 6

Galileo studied uniform acceleration by rolling balls down inclined ramps. He observed that a ball starting from rest would travel through $1,3,5,7,9,$ etc. units of distance during successive, equal time intervals. Explain why this observation is consistent with constant acceleration.

SK

Shubham Kumar

Numerade Educator

Problem 7

Given these graphs of velocity versus time for one-dimensional motion, construct graphs of position versus time and acceleration versus time.

Michael Sorola

Numerade Educator

Problem 8

Your car's maximum acceleration is about $3.0 \mathrm{~m} / \mathrm{s}^{2} .$ For about how long can it maintain that acceleration?

Luis Rios

Numerade Educator

Problem 9

A car going $25 \mathrm{~m} /$ s passes another going $20 \mathrm{~m} / \mathrm{s}$ in the same direction. What can you say about the accelerations of the two cars?

Luis Rios

Numerade Educator

Problem 10

A ball is launched straight up from the ground and falls straight back down. At any given position along the path, which of these quantities are the same and which are different for the upward and downward motions: velocity, speed, and acceleration?

Luis Rios

Numerade Educator

Problem 11

What can you say about an object's displacement during some time interval if its average velocity is zero during that interval? What can you say about the displacement if the average acceleration is zero?

Luis Rios

Numerade Educator

Problem 12

Zeno's paradox says that when going from a starting point to your destination, you first cover half the distance, then half the remaining distance (one-fourth the original distance), then half the remaining distance (one-eighth the original distance), and so on. Since each step takes you only halfway to your goal, you should never reach any destination. How would you refute Zeno's paradox?

Geena Pullo

Numerade Educator

Problem 13

If a trip from Earth to Moon (about $385,000 \mathrm{~km}$ ) takes 2.5 days, the average speed for the trip is (a) $1.8 \mathrm{~m} / \mathrm{s} ;$ (b) $29.7 \mathrm{~m} / \mathrm{s} ;$ (c) $1800 \mathrm{~m} / \mathrm{s}$ (d) $27,000 \mathrm{~m} / \mathrm{s}$.

Luis Rios

Numerade Educator

Problem 14

A cheetah can maintain its top speed of $32 \mathrm{~m} / \mathrm{s}$ for about $35 \mathrm{~s}$. During that time it travels about
(a) $750 \mathrm{~m} ;$ (b) $850 \mathrm{~m}$
(c) $1000 \mathrm{~m}$
(d) $1100 \mathrm{~m}$.

Luis Rios

Numerade Educator

Problem 15

For the first $1200 \mathrm{~m}$ of a 1500 -m race, a runner's average speed is $6.14 \mathrm{~m} / \mathrm{s}$. To finish in under 4 minutes, the runner's average speed for the remainder of the race must be at least (a) $6.73 \mathrm{~m} / \mathrm{s}$ (b) $7.14 \mathrm{~m} / \mathrm{s} ;$ (c) $8.05 \mathrm{~m} / \mathrm{s}$ : (d) $8.29 \mathrm{~m} / \mathrm{s}$.

Luis Rios

Numerade Educator

Problem 16

A runner sprints in the $+x$ -direction at $9.2 \mathrm{~m} / \mathrm{s}$ for $100 \mathrm{~m}$, stops, reverses direction, and jogs backward at $3.6 \mathrm{~m} / \mathrm{s}$ for $50 \mathrm{~m}$. The average velocity for the entire run is (a) $2.0 \mathrm{~m} / \mathrm{s}$; (b) $4.0 \mathrm{~m} / \mathrm{s}$; (c) $6.4 \mathrm{~m} / \mathrm{s}$ (d) $10.9 \mathrm{~m} / \mathrm{s}$.

Luis Rios

Numerade Educator

Problem 17

In one-dimensional motion, displacement (a) can never be negative; (b) can be positive, negative, or zero; (c) is the same as distance traveled; (d) can be greater than distance traveled.

Paul Gabriel

Numerade Educator

Problem 18

What's your average speed when you run at $4.0 \mathrm{~m} / \mathrm{s}$ for $60 \mathrm{~m}$ then at $6.0 \mathrm{~m} / \mathrm{s}$ for another $60 \mathrm{~m} ?$ (a) $4.8 \mathrm{~m} / \mathrm{s} ;$ (b) $5.0 \mathrm{~m} / \mathrm{s}$; (c) $5.2 \mathrm{~m} / \mathrm{s}$ (d) $5.4 \mathrm{~m} / \mathrm{s}$

Luis Rios

Numerade Educator

Problem 19

The average acceleration to boost a spacecraft from $1250 \mathrm{~m} / \mathrm{s}$ to $1870 \mathrm{~m} / \mathrm{s}$ in $35 \mathrm{~s}$ is
(a) $53.4 \mathrm{~m} / \mathrm{s}^{2}$
(b) $35.7 \mathrm{~m} / \mathrm{s}^{2}$
(c) $17.7 \mathrm{~m} / \mathrm{s}^{2}$
(d) $9.80 \mathrm{~m} / \mathrm{s}^{2}$

Luis Rios

Numerade Educator

Problem 20

Starting from rest, a go-cart undergoes constant acceleration $-1.4 \mathrm{~m} / \mathrm{s}^{2} .$ When its velocity reaches $-10 \mathrm{~m} / \mathrm{s},$ its displacement from its starting point is (a) $-7.14 \mathrm{~m}$; (b) $-14.3 \mathrm{~m} ;$ (c) $-35.7 \mathrm{~m}$ (d) $-100 \mathrm{~m}$.

Luis Rios

Numerade Educator

Problem 21

An arrow with speed $21.4 \mathrm{~m} / \mathrm{s}$ embeds itself $3.75 \mathrm{~cm}$ into a target before stopping. While in the target, its constant acceleration was (a) $-570 \mathrm{~m} / \mathrm{s}^{2}$; (b) $-1140 \mathrm{~m} / \mathrm{s}^{2}$; (c) $-6100 \mathrm{~m} / \mathrm{s}^{2}$ (d) $-12,200 \mathrm{~m} / \mathrm{s}^{2}$

Luis Rios

Numerade Educator

Problem 22

An object is dropped from rest off the $442-\mathrm{m}$ Sears Tower in Chicago. Its fall time is (a) $45.1 \mathrm{~s} ;$ (b) $19.1 \mathrm{~s} ;$ (c) $9.5 \mathrm{~s} ;$ (d) $4.7 \mathrm{~s}$.

Luis Rios

Numerade Educator

Problem 23

A ball dropped from rest from height $h$ reaches the ground with a speed $v$. If the drop height is changed to $2 h,$ its speed at the ground is (a) $4 v$ (b) $2 v ;$ (c) $\sqrt{2} v$; (d) $v$.

Paul Gabriel

Numerade Educator

Problem 24

You're driving at $12.8 \mathrm{~m} / \mathrm{s},$ and are $16.0 \mathrm{~m}$ from an intersection when you see a stoplight turn yellow. What acceleration do you need in order to just stop before the intersection?
(a) $-0.8 \mathrm{~m} / \mathrm{s}^{2}$
(b) $-5.1 \mathrm{~m} / \mathrm{s}^{2} ;$
(c) $-7.4 \mathrm{~m} / \mathrm{s}^{2}$
(d) $-10.2 \mathrm{~m} / \mathrm{s}^{2}$

Luis Rios

Numerade Educator

Problem 25

For an object traveling in a straight line with constant acceleration, the graph of its velocity versus time is (a) a horizontal line; (b) a diagonal line; (c) a parabola.

Luis Rios

Numerade Educator

Problem 26

A ball is thrown straight up from the ground at $10 \mathrm{~m} / \mathrm{s}$, and simultaneously a ball is thrown straight down from a 10 -m-high ledge at $10 \mathrm{~m} / \mathrm{s}$. At what height do the two balls pass? (a) $2.5 \mathrm{~m}$; (b) $3.2 \mathrm{~m} ;$ (c) $3.8 \mathrm{~m}$ (d) $5.0 \mathrm{~m}$.

Anand Jangid

Numerade Educator

Problem 27

In the example described by Figure $2.4,$ what are the displacement and total distance traveled for a round trip from your friend's house to the video store?

Paul Gabriel

Numerade Educator

Problem 28

Using the data in Conceptual Example $2.1,$ find the displacement for a trip from Lincoln to Grand Island. (Choose a coordinate system with the $+x$ -axis pointing east.)

Michael Sorola

Numerade Educator

Problem 29

Using the data in Conceptual Example $2.1,$ find the displacement and distance traveled for (a) $3,$ (b) $3 \frac{1}{2}$, and (c) $3 \frac{3}{4}$ round trips from Grand Island to Lincoln.

Michael Sorola

Numerade Educator

Problem 30

Find the average speed (in $\mathrm{m} / \mathrm{s}$ ) of a runner who completes each of the following races in the time given: (a) a marathon (41 $\mathrm{km}$ ) in 2 hours, 25 minutes; (b) $1500 \mathrm{~m}$ in 3 minutes, 50 seconds; (c) $100 \mathrm{~m}$ in $10.4 \mathrm{~s}$

Luis Rios

Numerade Educator

Problem 31

How much time does light from the Sun take to reach Earth? Use data from Appendix E.

Luis Rios

Numerade Educator

Problem 32

The best major league fastball goes about $44 \mathrm{~m} / \mathrm{s}$. (a) How much time does this pitch take to travel $18.4 \mathrm{~m}$ to home plate? (b) Make the same calculation for a "change-up" thrown at a speed of $32 \mathrm{~m} / \mathrm{s}$

Luis Rios

Numerade Educator

Problem 33

If you run at $4.0 \mathrm{~m} / \mathrm{s}$ for $100 \mathrm{~m},$ then at $5.0 \mathrm{~m} / \mathrm{s}$ for another $100 \mathrm{~m},$ what's your average speed?

Luis Rios

Numerade Educator

Problem 34

(a) Find your average speed if you go $10 \mathrm{~m} / \mathrm{s}$ for $100 \mathrm{~s}$ and then $20 \mathrm{~m} / \mathrm{s}$ for $100 \mathrm{~s}$. (b) Find your average speed if you go $10 \mathrm{~m} / \mathrm{s}$ for $1000 \mathrm{~m}$ and then $20 \mathrm{~m} / \mathrm{s}$ for $1000 \mathrm{~m}$. (c) Why are your
answers different?

Luis Rios

Numerade Educator

Problem 35

You are flying from Seattle to Anaheim with a connection in Oakland. The distance from Seattle to Oakland is $1100 \mathrm{~km},$ and Oakland to Anaheim is $550 \mathrm{~km}$. If both airplanes average $800 \mathrm{~km} / \mathrm{h}$ and the layover in Oakland is $80 \mathrm{~min}$, find (a) the total time for the trip and (b) your average speed.

Paul Gabriel

Numerade Educator

Problem 36

In a $2-\mathrm{km}$ crew race, boat 1 starts at $4.0 \mathrm{~m} / \mathrm{s}$ for the first $1500 \mathrm{~m},$ but slows to $3.1 \mathrm{~m} / \mathrm{s}$ for the rest of the race. Boat 2 goes a steady $3.6 \mathrm{~m} / \mathrm{s}$ for the first $1200 \mathrm{~m}$ and then $3.9 \mathrm{~m} / \mathrm{s}$ for the remainder. Who wins?

Anand Jangid

Numerade Educator

Problem 37

A plane flies east at $210 \mathrm{~km} / \mathrm{h}$ for $3.0 \mathrm{~h},$ then turns around and flies west at $170 \mathrm{~km} / \mathrm{h}$ for $2.0 \mathrm{~h}$. Taking the $+x$ -axis to point east, find the plane's average velocity and average speed for the trip.

Luis Rios

Numerade Educator

Problem 38

A runner is planning for a $10-\mathrm{km}$ race. She can maintain a steady speed of $4.10 \mathrm{~m} / \mathrm{s}$ for as much time as needed before ending the race with a $7.80-\mathrm{m} / \mathrm{s}$ sprint. If she wants to finish in 40 min or less, how far from the finish should she begin to sprint?

Paul Gabriel

Numerade Educator

Problem 39

In A dogsled goes straight at $9.5 \mathrm{~m} / \mathrm{s}$ for $10 \mathrm{~h}$. Then the dogs rest for the remainder of the day. What's the average velocity for the entire 24 -h day?

Willis James

Numerade Educator

Problem 40

A car travels a straight road at $100 \mathrm{~km} / \mathrm{h}$ for 30 min then at $60 \mathrm{~km} / \mathrm{h}$ for $10 \mathrm{~min}$. It then reverses and goes at $80 \mathrm{~km} / \mathrm{h}$ for 20 min. Find the average velocity and average speed for the entire trip.

Paul Gabriel

Numerade Educator

Problem 41

You're checking your car's speedometer. With cruise control engaged, the speedometer reads a constant $60 \mathrm{mi} / \mathrm{h}$. (a) Using highway mileposts, you clock $4 \mathrm{~min}, 45 \mathrm{~s}$ to go $5 \mathrm{~m}$. If the mileposts are accurate, what's the error in your speedometer reading? (b) How much time should you take to cover each mile if your true speed is $65 \mathrm{mi} / \mathrm{h} ?$

Manish Jain

Numerade Educator

Problem 42

On a windless day, a bird can fly at a constant $10 \mathrm{~m} / \mathrm{s}$. (a) It flies $10 \mathrm{~km}$ east and then home again. How much time does the round trip take? (b) A $5.0-\mathrm{m} / \mathrm{s}$ wind from the west gives the bird a groundspeed of $15 \mathrm{~m} / \mathrm{s}$ flying east and $5 \mathrm{~m} / \mathrm{s}$ flying west. Find the time for the round-trip flight under these conditions. (c) Compare your answers to parts (a) and (b). Why aren't they the same?

Narayan Hari

Numerade Educator

Problem 43

Chasing a zebra. A cheetah running at $30 \mathrm{~m} / \mathrm{s}$ is pursuing a zebra going in a straight line at $14 \mathrm{~m} / \mathrm{s}$. If the zebra has a $35-\mathrm{m}$ head start, how much time does it take for the cheetah to catch up?

Luis Rios

Numerade Educator

Problem 44

A parachutist free falls $440 \mathrm{~m}$ in $10.0 \mathrm{~s}$. She then opens her chute and drops the remaining $1350 \mathrm{~m}$. If her average velocity for the entire trip is $3.45 \mathrm{~m} / \mathrm{s}$, what's her average velocity while the chute is open?

Paul Gabriel

Numerade Educator

Problem 45

In $1675,$ the Danish astronomer Olaf Römer used observations of the eclipses of Jupiter's moons to estimate that it took the light about 22 min to cross the 299 -million-km diameter of Earth's orbit. Use Römer's data to compute the speed of light, and compare that with today's value of $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Luis Rios

Numerade Educator

Problem 46

Use the graph in Figure $\mathrm{P} 2.46$ to complete the next two problems.
In Find the average velocity over each 2.0 -s time interval, e.g., $0.0-2.0 \mathrm{~s}, 2.0-4.0 \mathrm{~s}$

Luis Rios

Numerade Educator

Problem 47

Use the graph in Figure $\mathrm{P} 2.46$ to complete the next two problems.
Construct a graph of velocity versus time for the entire time interval.

Luis Rios

Numerade Educator

Problem 48

For the next four problems, refer to Figure $\mathrm{P} 2.48$, a graph of velocity versus time for a car starting from rest on a straight road.
Find the average acceleration for each of the four intervals $(0-5 \mathrm{~s}, 5-10 \mathrm{~s},$ etc. $)$

Luis Rios

Numerade Educator

Problem 49

For the next four problems, refer to Figure $\mathrm{P} 2.48$, a graph of velocity versus time for a car starting from rest on a straight road.
Construct a graph of instantaneous acceleration from $t=0$ to $t=20 \mathrm{~s}$

Michael Sorola

Numerade Educator

Problem 50

For the next four problems, refer to Figure $\mathrm{P} 2.48$, a graph of velocity versus time for a car starting from rest on a straight road.
Draw a motion diagram for this trip.

Michael Sorola

Numerade Educator

Problem 51

Where is the acceleration (a) greatest, (b) least, and (c) zero? (d) Compute the greatest and least acceleration.

Paul Gabriel

Numerade Educator

Problem 52

For the sprinter described in Section $2.2,$ what's the average acceleration for the first half of the race?

Narayan Hari

Numerade Educator

Problem 53

The next three problems deal with a stock car, which starts from rest at time $t=0$ with velocity $(\mathrm{m} / \mathrm{s})$ increasing for $4.0 \mathrm{~s}$, according to the function $v_{x}=1.4 t^{2}+1.1 t$
(a) Find the car's velocity at the end of the $4.0-\mathrm{s}$ interval.
(b) Find the average acceleration for this interval.

Paul Gabriel

Numerade Educator

Problem 54

The next three problems deal with a stock car, which starts from rest at time $t=0$ with velocity $(\mathrm{m} / \mathrm{s})$ increasing for $4.0 \mathrm{~s}$, according to the function $v_{x}=1.4 t^{2}+1.1 t$
Graph the velocity as a function of time. When is the acceleration greatest and when is it least?

Paul Gabriel

Numerade Educator

Problem 55

The next three problems deal with a stock car, which starts from rest at time $t=0$ with velocity $(\mathrm{m} / \mathrm{s})$ increasing for $4.0 \mathrm{~s}$, according to the function $v_{x}=1.4 t^{2}+1.1 t$
Estimate the instantaneous acceleration at $t=2.0 \mathrm{~s}$.

Paul Gabriel

Numerade Educator

Problem 56

Draw a motion diagram for the car trip graphed in Figure $2.15 \mathrm{a}$

Michael Sorola

Numerade Educator

Problem 57

Draw a motion diagram for the car trip graphed in Figure $2.15 \mathrm{~b}$

Michael Sorola

Numerade Educator

Problem 58

Acceleration in blood flow. Figure $\mathrm{P} 2.58$ shows a pattern of coronary artery blood flow rates $(\mathrm{cm} / \mathrm{s})$ in a patient successfully treated for a myocardial infarction (heart attack). The upper and lower peaks represent the diastolic and systolic phases of the heartbeat. Estimate the average acceleration of the blood between the peaks of these phases.

Narayan Hari

Numerade Educator

Problem 59

You're driving at $50 \mathrm{~km} / \mathrm{h}$, when the traffic light $40 \mathrm{~m}$ away turns yellow. Find (a) the constant acceleration required to stop at the light and (b) the stopping time. Is the acceleration reasonable?

Luis Rios

Numerade Educator

Problem 60

Animal and human acceleration. (a) What constant acceleration is required for a cheetah to go from rest to its top speed of $90 \mathrm{~km} / \mathrm{h}$ in $3.0 \mathrm{~s}$ ? ( b) Repeat the calculation for a human who takes 2.0 s to reach a top speed of $10 \mathrm{~m} / \mathrm{s}$.

Luis Rios

Numerade Educator

Problem 61

A golfer putts her golf ball straight toward the hole. The ball's initial velocity is $2.52 \mathrm{~m} / \mathrm{s},$ and it accelerates at a rate of $-0.65 \mathrm{~m} / \mathrm{s}^{2}$. (a) Will the ball make it to the hole, $4.80 \mathrm{~m}$ away?
(b) If your answer is yes, what's the ball's velocity when it reaches the hole? If your answer is no, how close does it get before stopping?

Luis Rios

Numerade Educator

Problem 62

A rocket sled accelerates at $21.5 \mathrm{~m} / \mathrm{s}^{2}$ for $8.75 \mathrm{~s}$. (a) What's its velocity at the end of that time? (b) How far has it traveled?

Luis Rios

Numerade Educator

Problem 63

A car going initially with a velocity $13.5 \mathrm{~m} / \mathrm{s}$ accelerates at a rate of $1.9 \mathrm{~m} / \mathrm{s}^{2}$ for $6.2 \mathrm{~s}$. It then accelerates at a rate of $-1.2 \mathrm{~m} / \mathrm{s}^{2}$ until it stops. (a) Find the car's maximum speed. (b) Find the total time from the start of the first acceleration until the car is stopped. (c) What's the total distance the car travels?

Luis Rios

Numerade Educator

Problem 64

One car is going $50 \mathrm{~km} / \mathrm{h}$, another $100 \mathrm{~km} / \mathrm{h}$. Both have brakes that provide $-3.50 \mathrm{~m} / \mathrm{s}^{2}$ accelerations. (a) Find the stopping time for each car. (b) Find the stopping distance for each car. (c) Use your answer to part (a) to find the ratio of the stopping times, and use your answer to part (b) to find the ratio of the stopping distances.

Narayan Hari

Numerade Educator

Problem 65

A bullet going $310 \mathrm{~m} / \mathrm{s}$ strikes a 5.0 -cm-thick target. (a) What constant acceleration is required if the bullet is to stop within the target? (b) What's its acceleration if the bullet emerges from the target at $50 \mathrm{~m} / \mathrm{s} ?$

Luis Rios

Numerade Educator

Problem 66

A fully loaded 737 aircraft takes off at $250 \mathrm{~km} / \mathrm{h}$. If its acceleration is a steady $3.0 \mathrm{~m} / \mathrm{s}^{2},$ how long a runway is required? How much time does it take the plane to reach takeoff?

Luis Rios

Numerade Educator

Problem 67

A car is speeding at $75 \mathrm{mi} / \mathrm{h}(33.4 \mathrm{~m} / \mathrm{s})$. A police cruiser starts in pursuit from rest when the car is $100 \mathrm{~m}$ past the cruiser. At what rate must the cruiser accelerate to catch the speeder before the state line, $1.2 \mathrm{~km}$ away from the speeding car?

Luis Rios

Numerade Educator

Problem 68

An $x$ -ray tube accelerates electrons from rest at $5 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}$ through a distance of $15 \mathrm{~cm}$. Find (a) the electrons' velocity after this acceleration and (b) the acceleration time. (Such high accelerations are possible because electrons are extremely light.)

Luis Rios

Numerade Educator

Problem 69

A jet touches down at $310 \mathrm{~km} / \mathrm{h}(86.1 \mathrm{~m} / \mathrm{s})$. Find the (constant) acceleration required to stop the aircraft $1000 \mathrm{~m}$ down the runway.

Luis Rios

Numerade Educator

Problem 70

You're approaching an intersection at $50 \mathrm{~km} / \mathrm{h}(13.9 \mathrm{~m} / \mathrm{s})$ You see the light turn yellow when you're $35 \mathrm{~m}$ from the intersection. Assume a reaction time of 0.6 s before braking begins and a braking acceleration of $-3.0 \mathrm{~m} / \mathrm{s}^{2}$. (a) Will you be able to stop before the intersection? (b) The yellow light stays on for $3.4 \mathrm{~s}$ before turning red. If you continue at $50 \mathrm{~km} / \mathrm{h}$ without braking, will you make it through the $9.5-\mathrm{m}$ -wide intersection before the light turns red?

Narayan Hari

Numerade Educator

Problem 71

Disney's "Rockin' Roller Coaster" accelerates in a straight line from rest to $60 \mathrm{mi} / \mathrm{h}$ in $2.8 \mathrm{~s}$. (a) What is its (constant) acceleration? (b) How far does it travel during the first 2.8 s?

Luis Rios

Numerade Educator

Problem 72

Brain in juries in auto accidents. Brain injuries generally occur any time the brain's acceleration reaches $100 g$ for even a short time. Consider a car running into a solid barrier. With an airbag, the driver's head moves through a distance of $20 \mathrm{~cm}$ while the airbag stops it. Without an airbag, the head continues forward until the seatbelt stops the torso, causing the head to stop in a distance of only $5.0 \mathrm{~cm} .$ For each case, find the maximum speed with which the car can strike the barrier without causing brain injury.

Paul Gabriel

Numerade Educator

Problem 73

Jerry knocks a flowerpot off its third-story ledge, $9.5 \mathrm{~m}$ above the ground. If it falls freely, how fast is the flowerpot moving when it crashes to the sidewalk?

Luis Rios

Numerade Educator

Problem 74

After solving a difficult physics problem, an excited student throws his book straight up. It leaves his hand at $3.9 \mathrm{~m} / \mathrm{s}$ from $1.5 \mathrm{~m}$ above the ground. (a) How much time does it take until the book hits the floor? (b) What's its velocity then?

Paul Gabriel

Numerade Educator

Problem 75

The Jurassic Park ride at Universal Studios theme park drops $25.6 \mathrm{~m}$ straight down essentially from rest. Find the time for the drop and the velocity at the bottom.

Luis Rios

Numerade Educator

Problem 76

A batter pops the baseball straight up at $19.5 \mathrm{~m} / \mathrm{s}$. The catcher loses sight of the ball, so the first baseman has to rush in to catch it. How much time does he have?

Luis Rios

Numerade Educator

Problem 77

A rock is launched straight up from the ground at $16.5 \mathrm{~m} / \mathrm{s}$ Graph the rock's velocity and position versus time from launch until it reaches the ground.

Luis Rios

Numerade Educator

Problem 78

The gravitational acceleration of bodies dropped near the Moon's surface is about $1.6 \mathrm{~m} / \mathrm{s}^{2}$. Find the times for an object dropped from rest to fall $1.0 \mathrm{~m}$ on the Moon and on Earth.

Luis Rios

Numerade Educator

Problem 79

The first astronaut to reach Mars decides to measure the gravitational acceleration by dropping a rock from a $45.2-\mathrm{m}$ -high cliff. If the rock falls for $5.01 \mathrm{~s}$, what's $g_{\mathrm{Mars}}$ ?

Luis Rios

Numerade Educator

Problem 80

A tennis ball gun launches tennis balls at $18.5 \mathrm{~m} / \mathrm{s}$. It's pointed straight up and launches one ball; 2.0 s later, it launches a second ball. (a) At what time (after the first launch) are the two balls at the same height? (b) What is that height? (c) What are both balls' velocities at that point?

Manish Jain

Numerade Educator

Problem 81

A world-class volleyball player can jump vertically $1.1 \mathrm{~m}$ from a standing start. (a) How long is the player in the air? (b) Graph the athlete's position versus time. (c) Use your graph to explain why an athlete might appear to "hang" in the air near the top of the jump.

Michael Sorola

Numerade Educator

Problem 82

To escape a fire, you jump from a 2.5 -m-high window ledge. To cushion your landing, you begin with legs straight and end with your legs bent into a crouch $55 \mathrm{~cm}$ below your normal height. Find your (constant) acceleration upon striking the ground.

Paul Gabriel

Numerade Educator

Problem 83

A rocket accelerates straight up from the ground at $12.6 \mathrm{~m} / \mathrm{s}^{2}$ for $11.0 \mathrm{~s}$. Then the engine cuts off and the rocket enters free fall.
(a) Find its velocity at the end of its upward acceleration. (b) What maximum height does it reach? (c) With what velocity does it crash to Earth? (d) What's the total time from launch to crash?

Luis Rios

Numerade Educator

Problem 84

A ball thrown straight up from the ground passes a window $5.6 \mathrm{~m}$ up. An observer looking out the window sees the ball pass the window again, going down, $3.2 \mathrm{~s}$ later. Find (a) the velocity with which the ball was initially thrown and (b) the total time for the round trip, from the time the ball was thrown until it reaches the ground.

Manish Jain

Numerade Educator

Problem 85

In lab, a student measures an acceleration of $3.50 \mathrm{~m} / \mathrm{s}^{2}$ for a ball rolling down a 30 -degree incline. Then the ball rolls up a 45-degree incline, reaching the same height from which it was released (Figure $\mathrm{P} 2.85) .$ Find the ball's acceleration along the second ramp.

Paul Gabriel

Numerade Educator

Problem 86

A helicopter rises vertically with a constant upward acceleration of $0.40 \mathrm{~m} / \mathrm{s}^{2}$. As it passes an altitude of $20 \mathrm{~m}$, a wrench slips out the door. (a) How soon and (b) at what speed does the wrench hit the ground?

Luis Rios

Numerade Educator

Problem 87

For the situation in the preceding problem, let $t=0$ be the moment when the wrench slips from the helicopter. Draw graphs of position and velocity versus time for the wrench, from until it hits the ground.

Michael Sorola

Numerade Educator

Problem 88

Jumping flea. For its size, the flea can jump to amazing heights - as high as $30 \mathrm{~cm}$ straight up, about 100 times the flea's length.
(a) For such a jump, what takeoff speed is required?
(b) How much time does it take the flea to reach maximum height? (c) The flea accomplishes this leap using its extremely elastic legs. Suppose its upward acceleration is constant while it thrusts through a distance of $0.90 \mathrm{~mm}$. What's the magnitude of that acceleration? Compare with $g$.

Michael Sorola

Numerade Educator

Problem 89

Falling cat. Young cats develop a "righting reflex" that enables them to land on their feet after a fall. Upon landing they absorb the impact by extending their feet and then crouching after their feet touch the ground. (a) Find the speed with which a cat reaches the ground after a fall from a 6.4 -m-high window. (b) After this cat touches the ground, it comes to rest with a constant acceleration as it crouches through a distance of $14 \mathrm{~cm} .$ Find the acceleration during the crouching maneuver.

Narayan Hari

Numerade Educator

Problem 90

Starting from rest on your bicycle, you go in a straight line with acceleration $2.0 \mathrm{~m} / \mathrm{s}^{2}$ for $5.0 \mathrm{~s}$. Then you pedal with a constant velocity for another $5.0 \mathrm{~s}$. (a) What's your final velocity? (b) What is the total distance cycled? (c) Draw graphs of position and velocity versus time for the entire trip.

Michael Sorola

Numerade Educator

Problem 91

You're driving at a legal $13.4 \mathrm{~m} / \mathrm{s}$, and you're $15.0 \mathrm{~m}$ from an intersection when you see a stoplight turn yellow.
(a) What acceleration do you need to stop at the intersection?
(b) What's the corresponding stopping time? (c) Repeat part (a), but now assume a reaction time of 0.60 s before you brake.

Narayan Hari

Numerade Educator

Problem 92

The graph in Figure GP2.92 shows velocity versus time for a ball projected upward along an incline. Take the $+x$ -axis directed upward along the incline. (a) Describe what you would see if you were watching this ball. (b) How far up the ramp does the ball get from its initial position? (c) Graph the acceleration and position versus time for the rolling ball.

Paul A.

California State Polytechnic University, Pomona

Problem 93

You're driving down a straight highway at $25 \mathrm{~m} / \mathrm{s}$. You apply the brakes and stop after $10.0 \mathrm{~s}$ of constant acceleration.
(a) Graph (a) your velocity and (b) your position, both versus time. (c) Draw a motion diagram, showing your car at 2.0 -s intervals.

Michael Sorola

Numerade Educator

Problem 94

A ball rolls up an incline with initial speed $2.40 \mathrm{~m} / \mathrm{s}$. Exactly 6.0 s later, it passes back down through the launch point. Draw a graph of (a) velocity and (b) position versus time for the entire trip, with $x=0$ being the launch point and the positive $x$ -axis pointing up the ramp. (c) Find the ball's average velocity and average speed for the entire trip.

CA

Chi-Chung Ai

Numerade Educator

Problem 95

You throw a baseball straight up at $12.1 \mathrm{~m} / \mathrm{s}$. (a) Find the time(s) when the ball is $5.20 \mathrm{~m}$ above its launch point. (b) Find the velocity at each time you found in part (a).

Paul Gabriel

Numerade Educator

Problem 96

A student throws a baseball straight up from $1.50 \mathrm{~m}$ above the ground with a speed of $11.0 \mathrm{~m} / \mathrm{s}$. Simultaneously, another student on top of the 12.6 -m-high physics building throws a baseball straight down at $11.0 \mathrm{~m} / \mathrm{s}$. When and where do the two balls meet?

Manish Jain

Numerade Educator

Problem 97

A "moving sidewalk" in an airport runs at a constant $1.0 \mathrm{~m} / \mathrm{s}$. From opposite ends of the 50 -m-long sidewalk, two old friends begin running toward one another, each with a speed of $4.0 \mathrm{~m} / \mathrm{s}$ relative to the moving sidewalk. Where do they meet, relative to the fixed ends of the sidewalk?

Manish Jain

Numerade Educator

Problem 98

Cheetah chase. A cheetah can accelerate from rest to $60 \mathrm{mph}$ in $3.0 \mathrm{~s}$. (a) Find the cheetah's (assumed constant) acceleration in SI units. (b) Although they're fast, cheetahs tire quickly. A gazelle running at a constant $20 \mathrm{~m} / \mathrm{s}$ has a $25-\mathrm{m}$ head start on a resting cheetah. The cheetah runs toward the gazelle, accelerating from rest to $60 \mathrm{mph}$ in $3.0 \mathrm{~s}$ and then maintaining that speed for 10 s before tiring. Does the cheetah catch the gazelle?

Narayan Hari

Numerade Educator

Problem 99

Runner A leads runner B by $85.0 \mathrm{~m}$ in a distance race, and both are running at $4.45 \mathrm{~m} / \mathrm{s}$. Runner $\mathrm{B}$ accelerates at $0.10 \mathrm{~m} / \mathrm{s}^{2}$ for the next $10 \mathrm{~s}$ and then runs with constant velocity. How much total time elapses before B passes A?

Manish Jain

Numerade Educator

Problem 100

At the edge of a 12 -m-tall building, two children throw rocks at $10 \mathrm{~m} / \mathrm{s}$, one upward and one downward. (a) Find the time until each rock hits the ground. (b) Find the speed of each when it hits.

Narayan Hari

Numerade Educator

Problem 101

A train passes through a station at a constant $11 \mathrm{~m} / \mathrm{s}$. On a parallel track sits another train at rest. At the moment the first train passes, the second begins to accelerate at $1.5 \mathrm{~m} / \mathrm{s}^{2}$. When and where do the trains meet again?

Manish Jain

Numerade Educator

Problem 102

Two 110 -m-long trains are traveling at $22.5 \mathrm{~m} / \mathrm{s}$, going in opposite directions on parallel tracks. (a) How much time elapses from the moment the front ends of the trains pass to when the rear ends pass? (b) Repeat part (a), but this time suppose that when the front ends pass, one train begins to accelerate at $1.0 \mathrm{~m} / \mathrm{s}^{2}$

Manish Jain

Numerade Educator

Problem 103

Attempting to waste the last $4.8 \mathrm{~s}$ of a basketball game, a player on the team that's ahead throws the ball straight up. He releases it $1.6 \mathrm{~m}$ above the ground, and an opposing player catches it at the same height on the way down. The ball isn't permitted to touch the roof, $17.2 \mathrm{~m}$ above the ground. Did the winning team run out the clock, or will the opponent have time to make a shot?

SK

Shubham Kumar

Numerade Educator