College Physics: A Strategic Approach

Randall D. Knight, Brian Jones, Stuart Field

Chapter 2

Motion in One Dimension - all with Video Answers

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Chapter Questions

Problem 1

Figure P2. I shows a motion diagram of a car traveling down a street. The camera took one frame every second. A distance scale is provided. a. Measure the $x$ -value of the car at each dot. Place your data in a table, similar to Table $2.1,$ showing each position and the instant of time at which it occurred.
b. Make a graph of $x$ versus $t,$ using the data in your table. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.

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Problem 2

For each motion diagram in Figure P2.2, determine the sign (positive or negative) of the position and the velocity.

Supratim Pal

Numerade Educator

Problem 3

The position graph of Figure $\mathrm{P} 2.3$ shows a dog slowly sneaking up on a squirrel, then putting on a burst of speed.
a. For how many seconds does the dog move at the slower speed?
b. Draw the dog's velocity-versus-time graph. Include a numerical scale on both axes.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 4

A rural mail carrier is driving slowly, putting mail in mailboxes near the road. He overshoots one mailbox, stops, shifts into reverse, and then backs up until he is at the right spot. The velocity graph of Figure $\mathrm{P} 2.4$ represents his motion.
a. Draw the mail carrier's position-versus-time graph. Assume that $x=0 \mathrm{m}$ at $t=0 \mathrm{s}$
b. What is the position of the mailbox?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 5

For the velocity-versus-time graph of Figure $\mathrm{P} 2.5:$ a. Draw the corresponding position-versus-time graph. Assume that $x=0 \mathrm{m}$ at $t=0 \mathrm{s}$
b. What is the object's position at $t=12 \mathrm{s} ?$
c. Describe a moving object that could have these graphs.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 6

II A bicyclist has the position-versus-time graph shown in Figure $\mathrm{P} 2.6 .$ What is the bicyclist's velocity at $t=10 \mathrm{s},$ at $t=25 \mathrm{s},$ and at $t=35 \mathrm{s} ?$

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Problem 7

In major league baseball, the pitcher's mound is 60 feet from the batter. If a pitcher throws a 95 mph fastball, how much time elapses from when the ball leaves the pitcher's hand until the ball reaches the batter?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 8

In college softball, the distance from the pitcher's mound to the batter is 43 feet. If the ball leaves the bat at $100 \mathrm{mph}$, how much time elapses between the hit and the ball reaching the pitcher?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 9

Alan leaves Los Angeles at 8: 00 AM to drive to San Francisco, $400 \mathrm{mi}$ away. He travels at a steady $50 \mathrm{mph}$. Beth leaves Los Angeles at 9: 00 . AM and drives a steady 60 mph.
a. Who gets to San Francisco first?
b. How long does the first to arrive have to wait for the second?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 10

Richard is driving home to visit his parents. $125 \mathrm{mi}$ of the trip are on the interstate highway where the speed limit is $65 \mathrm{mph}$. Normally Richard drives at the speed limit; but today he is running late and decides to take his chances by driving at 70 mph. How many minutes does he save?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 11

In a $5.00 \mathrm{km}$ race, one runner runs at a steady $12.0 \mathrm{km} / \mathrm{h}$ and another runs at $14.5 \mathrm{km} / \mathrm{h}$. How long does the faster runner have to wait at the finish line to see the slower runner cross?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 12

In an $8.00 \mathrm{km}$ race, one runner runs at a steady $11.0 \mathrm{km} / \mathrm{h}$ and another runs at $14.0 \mathrm{km} / \mathrm{h}$. How far from the finish line is the slower runner when the faster runner finishes the race?

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Problem 13

A car moves with constant velocity along a straight road. Its position is $x_{1}=0 \mathrm{m}$ at $t_{1}=0 \mathrm{s}$ and is $x_{2}=30 \mathrm{m}$ at $t_{2}=3.0 \mathrm{s}$
Answer the following by considering ratios, without computing the car's velocity.
a. What is the car's position at $t=1.5 \mathrm{s} ?$
b. What will be its position at $t=9.0 \mathrm{s} ?$

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Problem 14

While running a marathon, a long-distance runner uses a stopwatch to time herself over a distance of $100 \mathrm{m}$. She finds that she runs this distance in 18 s. Answer the following by considering ratios, without computing her velocity.
a. If she maintains her speed, how much time will it take her to run the next $400 \mathrm{m} ?$
b. How long will it take her to run a mile at this speed?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 15

Figure $\mathrm{P} 2.15$ shows the position graph of a particle.
a. Draw the particle's velocity graph for the interval $0 \mathrm{s} \leq t \leq 4 \mathrm{s}$
b. Does this particle have a turning point or points? If so, at what time or times?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 16

A somewhat idealized graph of the speed of the blood in the ascending aorta during one beat of the heart appears as in Figure P2.16.
a. Approximately how far, in $\mathrm{cm},$ does the blood move during one beat?
b. Assume similar data for the motion of the blood in your aorta, and make a rough estimate of the distance from your heart to your brain. Estimate how many beats of the heart it takes for blood to travel from your heart to your brain.

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Problem 17

A car starts from $x_{i}=10 \mathrm{m}$ at $t_{i}=0 \mathrm{s}$ and moves with the velocity graph shown in Figure $\mathrm{P} 2.17$.
a. What is the car's position at $t=2 \mathrm{s}, 3 \mathrm{s},$ and $4 \mathrm{s} ?$
b. Does this car ever change direction? If so, at what time?

Supratim Pal

Numerade Educator

Problem 18

Figure P2.18 shows a graph of actual position-versus-time data for a particular type of drag racer known as a "funny car."
a. Estimate the car's velocity at $2.0 \mathrm{s}$.
b. Estimate the car's velocity at $4.0 \mathrm{s}$.

Vishal Gupta

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Problem 19

Figure P2.19 shows the velocity graph of a bicycle. Draw the bicycle's acceleration graph for the interval $0 \mathrm{s} \leq t \leq 4 \mathrm{s}$. Give both axes an appropriate numerical scale.

Brandy Heflin

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Problem 20

We set the origin of a coordinate system so that the position of a train is $x=0 \mathrm{m}$ at $t=0$ s. Figure $\mathrm{P} 2.20$ shows the train's velocity graph.
a. Draw position and acceleration graphs for the train.
b. Find the acceleration of the train at $t=3.0 \mathrm{s}$.

Supratim Pal

Numerade Educator

Problem 21

For each motion diagram shown earlier in Figure $\mathrm{P} 2.2$, determine the sign (positive or negative) of the acceleration.

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Problem 22

Figure P2.16 showed data for the speed of blood in the aorta. Determine the magnitude of the acceleration for both phases, speeding up and slowing down.

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Problem 23

Figure $\mathrm{P} 2.23$ is a somewhat simplified velocity graph for Olympic sprinter Carl Lewis starting a $100 \mathrm{m}$ dash. Estimate his acceleration during each of the intervals $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$.

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Problem 24

Small frogs that are good jumpers are capable of remarkable accelerations. One species reaches a takeoff speed of $3.7 \mathrm{m} / \mathrm{s}$ in $60 \mathrm{ms} .$ What is the frog's acceleration during the jump?

Vishal Gupta

Numerade Educator

Problem 25

A Thomson's gazelle can reach a speed of $13 \mathrm{m} / \mathrm{s}$ in $3.0 \mathrm{s}$. A lion can reach a speed of $9.5 \mathrm{m} / \mathrm{s}$ in $1.0 \mathrm{s}$. A trout can reach a speed of $2.8 \mathrm{m} / \mathrm{s}$ in $0.12 \mathrm{s}$. Which animal has the largest acceleration?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 26

When striking, the pike, a predatory fish, can accelerate from rest to a speed of $4.0 \mathrm{m} / \mathrm{s}$
in $0.11 \mathrm{s}$
a. What is the acceleration of the pike during this strike?
b. How far does the pike move during this strike?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 27

a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?
b. What fraction of $g$ is this?
c. How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 28

When jumping, a flea rapidly extends its legs, reaching a takeoff speed of $1.0 \mathrm{m} / \mathrm{s}$ over a distance of $0.50 \mathrm{mm} .$
a. What is the flea's acceleration as it extends its legs?
b. How long does it take the flea to leave the ground after it begins pushing off?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 29

A car traveling at speed $v$ takes distance $d$ to stop after the brakes are applied. What is the stopping distance if the car is initially traveling at speed $2 v ?$ Assume that the acceleration due to the braking is the same in both cases.

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Problem 30

Light-rail passenger trains that provide transportation within and between cities speed up and slow down with a nearly constant (and quite modest) acceleration. A train travels through a congested part of town at $5.0 \mathrm{m} / \mathrm{s}$. Once free of this area, it speeds up to $12 \mathrm{m} / \mathrm{s}$ in $8.0 \mathrm{s}$. At the edge of town, the driver again accelerates, with the same acceleration, for another $16 \mathrm{s}$ to reach a higher cruising speed. What is the final speed?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 31

A cross-country skier is skiing along at a zippy $8.0 \mathrm{m} / \mathrm{s}$. She stops pushing and simply glides along, slowing to a reduced speed of $6.0 \mathrm{m} / \mathrm{s}$ after gliding for $5.0 \mathrm{m} .$ What is the magnitude of her acceleration as she slows?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 32

A small propeller airplane can comfortably achieve a high enough speed to take off on a runway that is $1 / 4$ mile long. $A$ large, fully loaded passenger jet has about the same acceleration from rest, but it needs to achieve twice the speed to take off. What is the minimum runway length that will serve? Hint: You can solve this problem using ratios without having any additional information.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 33

Formula One racers speed up much more quickly than normal passenger vehicles, and they also can stop in a much shorter distance. A Formula One racer traveling at $90 \mathrm{m} / \mathrm{s}$ can stop in a distance of $110 \mathrm{m}$. What is the magnitude of the car's acceleration as it slows during braking?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 34

Figure $\mathrm{P} 2.34$ shows a velocity-versus-time graph for a particle moving along the $x$ -aris. At $t=0$ s, assume that $x=0$ m.
a. What are the particle's position, velocity, and acceleration at $t=1.0 \mathrm{s} ?$
b. What are the particle's position, velocity, and acceleration at $t=3.0 \mathrm{s} ?$

Supratim Pal

Numerade Educator

Problem 35

A driver has a reaction time of $0.50 \mathrm{s}$, and the maximum deceleration of her car is $6.0 \mathrm{m} / \mathrm{s}^{2} .$ She is driving at $20 \mathrm{m} / \mathrm{s}$ when suddenly she sees an obstacle in the road $50 \mathrm{m}$ in front of her. Can she stop the car in time to avoid a collision?

Mayukh Banik

Numerade Educator

Problem 36

Chameleons catch insects with their tongues, which they can rapidly extend to great lengths. In a typical strike, the chameleon's tongue accelerates at a remarkable $250 \mathrm{m} / \mathrm{s}^{2}$ for $20 \mathrm{ms},$ then travels at constant speed for another 30 ms. During this total time of $50 \mathrm{ms}, 1 / 20$ of a second, how far does the tongue reach?

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Problem 37

You're driving down the highway late one night at $20 \mathrm{m} / \mathrm{s}$ when a deer steps onto the road $35 \mathrm{m}$ in front of you. Your reaction time before stepping on the brakes is $0.50 \mathrm{s},$ and the maximum deceleration of your car is $10 \mathrm{m} / \mathrm{s}^{2}$.
a. How much distance is between you and the deer when you come to a stop?
b. What is the maximum speed you could have and still not hit the deer?

Mayukh Banik

Numerade Educator

Problem 38

A light-rail train going from one station to the next on a straight section of track accelerates from rest at $1.1 \mathrm{m} / \mathrm{s}^{2}$ for $20 \mathrm{s}$. It then proceeds at constant speed for $1100 \mathrm{m}$ before slowing down at $2.2 \mathrm{m} / \mathrm{s}^{2}$ until it stops at the station.
What is the distance between the stations?
b. How much time does it take the train to go between the stations?

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Problem 39

A car is traveling at a steady $80 \mathrm{km} / \mathrm{h}$ in a $50 \mathrm{km} / \mathrm{h}$ zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady $8.0 \mathrm{m} / \mathrm{s}^{2}$
a. How much time elapses before the motorcycle is moving as fast as the car?
b. How far is the motorcycle from the car when it reaches this speed?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 40

When a jet lands on an aircraft carrier, a hook on the tail of the plane grabs a wire that quickly brings the plane to a halt before it overshoots the deck. In a typical landing, a jet touching down at $240 \mathrm{km} / \mathrm{h}$ is stopped in a distance of $95 \mathrm{m}$.
a. What is the magnitude of the jet's acceleration as it is brought to rest?
b. How much time does the landing take?

Narayan Hari

Numerade Educator

Problem 41

A simple model for a person running the $100 \mathrm{m}$ dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line. If a sprinter reaches his top speed of $11.2 \mathrm{m} / \mathrm{s}$ in $2.14 \mathrm{s},$ what will be his total time?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 42

Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower-called a shot tower-and
solidify as they fall.
If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?
b. What is the bearing's impact velocity?

Mayukh Banik

Numerade Educator

Problem 43

Here's an interesting challenge you can give to a friend. Hold a $\$ 1$ (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it's not. After she sees that you have released the bill, it will take her about $0.25 \mathrm{s}$ to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is $16 \mathrm{cm}$.

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Problem 44

In the preceding problem we saw that a person's reaction time is generally not quick enough to allow the person to catch a \$1 bill dropped between the fingers. The $16 \mathrm{cm}$ length of the bill passes through a student's fingers before she can grab it if she has a typical 0.25 s reaction time. How long would a bill need to be for her to have a good chance of catching it?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 45

A gannet is a seabird that fishes by diving from a great height. If a gannet hits the water at $32 \mathrm{m} / \mathrm{s}$ (which they do), what height did it dive from? Assume that the gannet was motionless before starting its dive.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 46

A student at the top of a building of height $h$ throws ball A straight upward with speed $v_{0}$ and throws ball $B$ straight downward with the same initial speed.
a. Compare the balls' accelerations, both direction and magnitude, immediately after they leave her hand. Is one acceleration larger than the other? Or are the magnitudes equal?
b. Compare the final speeds of the balls as they reach the ground. Is one larger than the other? Or are they equal?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 47

Excellent human jumpers can leap straight up to a height of $110 \mathrm{cm}$ off the ground. To reach this height, with what speed would a person need to leave the ground?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 48

A football is kicked straight up into the air, it hits the ground 5.2 s later.
a. What was the greatest height reached by the ball? Assume it is kicked from ground level.
b. With what speed did it leave the kicker's foot?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 49

In an action movie, the villain is rescued from the ocean by grabbing onto the ladder hanging from a helicopter. He is so intent on gripping the ladder that he lets go of his briefcase of counterfeit money when he is $130 \mathrm{m}$ above the water. If the briefcase hits the water 6.0 s later, what was the speed at which the helicopter was ascending?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 50

Spud Webb was, at 5 ft 8 in, one of the shortest basketball players to play in the NBA. But he had an amazing vertical leap; he could jump to a height of $1.1 \mathrm{m}$ off the ground, so he could easily dunk a basketball. For such a leap, what was his "hang time"-the time spent in the air after leaving the ground and before touching down again?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 51

A rock climber stands on top of a 50-m-high cliff overhanging a pool of water. He throws two stones vertically downward $1.0 \mathrm{s}$ apart and observes that they cause a single splash. The initial speed of the first stone was $2.0 \mathrm{m} / \mathrm{s}$.
a. How long after the release of the first stone does the second stone hit the water?
b. What was the initial speed of the second stone?
c. What is the speed of each stone as it hits the water?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 52

Actual velocity data for a lion pursuing prey are shown in Figure P2.52. Estimate:
a. The initial acceleration of the lion.
b. The acceleration of the lion at $2 \mathrm{s}$ and at $4 \mathrm{s}$.
c. The distance traveled by the lion between $0 \mathrm{s}$ and $8 \mathrm{s}$.

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Problem 53

A truck driver has a shipment of apples to deliver to a destination 440 miles away. The trip usually takes him 8 hours. Today he finds himself daydreaming and realizes 120 miles into his trip that he is running 15 minutes later than his usual pace at this point. At what speed must he drive for the remainder of the trip to complete the trip in the usual amount of time?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 54

When you sneeze, the air in your lungs accelerates from rest to approximately $150 \mathrm{km} / \mathrm{h}$ in about 0.50 seconds.
What is the acceleration of the air in $\mathrm{m} / \mathrm{s}^{2}$ ?
b. What is this acceleration, in units of $g ?$

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Problem 55

Figure $\mathrm{P} 2.55$ shows the motion diagram, made at two frames of film per second, of a ball rolling along a track. The track has a $3.0-\mathrm{m}$ -long sticky section.
a. Use the scale to determine the positions of the center of the ball. Place your data in a table, similar to Table $2.1,$ showing each position and the instant of time at which it occurred.
b. Make a graph of $x$ versus $t$ for the ball. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.
c. What is the change in the ball's position from $t=0$ s to $t=1.0 \mathrm{s} ?$
d. What is the change in the ball's position from $t=2.0 \mathrm{s}$ to $t=4.0 \mathrm{s} ?$
e. What is the ball's velocity before reaching the sticky section?
f. What is the ball's velocity after passing the sticky section?
g. Determine the ball's acceleration on the sticky section of the track.

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Problem 56

Julie drives $100 \mathrm{mi}$ to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 40 mph and half the distance at $60 \mathrm{mph}$. On her return trip, she drives half the time at 40 mph and half the time at 60 mph.
a. How long does it take Julie to complete the trip to Grandmother's house?
b. How long does the return trip take?

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Problem 57

The takeoff speed for an Airbus A320 jetliner is $80 \mathrm{m} / \mathrm{s}$. Velocity data measured during takeoff are as shown in the table.
What is the jetliner's acceleration during takeoff, in $\mathrm{m} / \mathrm{s}^{2}$ and in $g$ 's?
b. At what time do the wheels leave the ground?
c. For safety reasons, in case of an aborted takeoff, the length of the runway must be three times the takeoff distance. What is the minimum length runway this aircraft can use?
$$\begin{array}{cc}t(\mathrm{s}) & v_{x}(\mathrm{m} / \mathrm{s}) \\\hline 0 & 0 \\10 & 23 \\20 & 46 \\30 & 69 \\
\hline\end{array}$$

Krystal K

Numerade Educator

Problem 58

Does a real automobile have constant acceleration? Measured data for a Porsche 944 Turbo at maximum acceleration are as shown in the table.
a. Convert the velocities to $\mathrm{m} / \mathrm{s}$, then make a graph of velocity versus time. Based on your graph, is the acceleration constant? Explain.
b. Draw a smooth curve through the points on your graph, then use your graph to estimate the car's acceleration at $2.0 \mathrm{s}$ and $8.0 \mathrm{s}$. Give your answer in SI units. Hint: Remember that acceleration is the
slope of the velocity graph.

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Problem 59

People hoping to travel to other worlds are faced with huge challenges. One of the biggest is the time required for a journey. The nearest star is $4.1 \times 10^{16} \mathrm{m}$ away. Suppose you had a spacecraft that could accelerate at $1.0 \mathrm{g}$ for half a year, then continue at a constant speed. (This is far beyond what can be achieved with any known technology.) How long would it take you to reach the nearest star to earth?

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Problem 60

You are driving to the grocery store at $20 \mathrm{m} / \mathrm{s}$. You are $110 \mathrm{m}$ from an intersection when the traffic light turns red. Assume that your reaction time is 0.70 s and that your car brakes with constant acceleration.
a. How far are you from the intersection when you begin to apply the brakes?
b. What acceleration will bring you to rest right at the intersection?
c. How long does it take you to stop?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 61

When you blink your eye, the upper lid goes from rest with your eye open to completely covering your eye in a time of $0.024 \mathrm{s}$
a. Estimate the distance that the top lid of your eye moves during a blink.
b. What is the acceleration of your eyelid? Assume it to be constant.
c. What is your upper eyelid's final speed as it hits the bottom eyelid?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 62

A bush baby, an African primate, is capable of a remarkable vertical leap. The bush baby goes into a crouch and extends its legs, pushing upward for a distance of $0.16 \mathrm{m} .$ After this upward acceleration, the bush baby leaves the ground and travels upward for $2.3 \mathrm{m}$. What is the acceleration during the pushing-off phase? Give your answer in $\mathrm{m} / \mathrm{s}^{2}$ and in $g$ 's.

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Problem 63

When jumping, a flea reaches a takeoff speed of $1.0 \mathrm{m} / \mathrm{s}$ over a distance of $0.50 \mathrm{mm}$.
a. What is the flea's acceleration during the jump phase?
b. How long does the acceleration phase last?
c. If the flea jumps straight up, how high will it go? (Ignore air resistance for this problem; in reality, air resistance plays a large role, and the flea will not reach this height.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 64

Certain insects can achieve seemingly impossible accelerations while jumping. The click beetle accelerates at an astonishing $400 g$ over a distance of $0.60 \mathrm{cm}$ as it rapidly bends its thorax, making the "click" that gives it its name.
a. Assuming the beetle jumps straight up, at what speed does it leave the ground?
b. How much time is required for the beetle to reach this speed?
c. Ignoring air resistance, how high would it go?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 65

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of $15 \mathrm{m} / \mathrm{s}$ when the hand is $2.0 \mathrm{m}$ above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 66

A rock is tossed straight up with a speed of $20 \mathrm{m} / \mathrm{s}$. When it returns, it falls into a hole $10 \mathrm{m}$ deep.
a. What is the rock's velocity as it hits the bottom of the hole?
b. How long is the rock in the air, from the instant it is released until it hits the bottom of the hole?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 67

A 200 kg weather rocket is loaded with $100 \mathrm{kg}$ of fuel and fired straight up. It accelerates upward at $30.0 \mathrm{m} / \mathrm{s}^{2}$ for $30.0 \mathrm{s}$, then runs out of fuel. Ignore any air resistance effects.
a. What is the rocket's maximum altitude?
b. How long is the rocket in the air?
c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.

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Problem 68

A hotel elevator ascends $200 \mathrm{m}$ with a maximum speed of $5.0 \mathrm{m} / \mathrm{s} .$ Its acceleration and deceleration both have a magnitude of $1.0 \mathrm{m} / \mathrm{s}^{2}$
a. How far does the elevator move while accelerating to full speed from rest?
b. How long does it take to make the complete trip from bottom to top?

Mayukh Banik

Numerade Educator

Problem 69

A car starts from rest at a stop sign. It accelerates at $2.0 \mathrm{m} / \mathrm{s}^{2}$ for 6.0 seconds, coasts for $2.0 \mathrm{s},$ and then slows down at a rate of $1.5 \mathrm{m} / \mathrm{s}^{2}$ for the next stop sign. How far apart are the stop signs?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 70

A toy train is pushed forward and released at $x_{i}=2.0 \mathrm{m}$ with a speed of $2.0 \mathrm{m} / \mathrm{s}$. It rolls at a steady speed for $2.0 \mathrm{s}$, then one wheel begins to stick. The train comes to a stop $6.0 \mathrm{m}$ from the point at which it was released. What is the train's acceleration after its wheel begins to stick?

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Problem 71

Heather and Jerry are standing on a bridge $50 \mathrm{m}$ above a river. Heather throws a rock straight down with a speed of $20 \mathrm{m} / \mathrm{s}$. Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.
a. How much time elapses between the first splash and the second splash?
b. Which rock has the faster speed as it hits the water?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 72

A Thomson's gazelle can run at very high speeds, but its acceleration is relatively modest. A reasonable model for the sprint of a gazelle assumes an acceleration of $4.2 \mathrm{m} / \mathrm{s}^{2}$ for $6.5 \mathrm{s}$, after which the gazelle continues at a steady speed.
a. What is the gazelle's top speed?
b. A human would win a very short race with a gazelle. The best time for a $30 \mathrm{m}$ sprint for a human runner is $3.6 \mathrm{s}$. How much time would the gazelle take for a $30 \mathrm{m}$ race?
c. A gazelle would win a longer race. The best time for a $200 \mathrm{m}$ sprint for a human runner is 19.3 s. How much time would the gazelle take for a $200 \mathrm{m}$ race?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 73

We've seen that a man's higher initial acceleration means that a man can outrun a horse over a very short race. A simple-but plausible -model for a sprint by a man and a horse uses the following assumptions: The man accelerates at $6.0 \mathrm{m} / \mathrm{s}^{2}$ for $1.8 \mathrm{s}$ and then runs at a constant speed. A horse accelerates at a more modest $5.0 \mathrm{m} / \mathrm{s}^{2}$ but continues accelerating for $4.8 \mathrm{s}$ and then continues at a constant speed. A man and a horse are competing in a $200 \mathrm{m}$ race. The man is given a $100 \mathrm{m}$ head start, so he begins $100 \mathrm{m}$ from the finish line. How much time does the man take to complete the race? How much time does the horse take? Who wins the race?

00000 00000

Numerade Educator

Problem 74

A pole-vaulter is nearly motionless as he clears the bar, set $4.2 \mathrm{m}$ above the ground. He then falls onto a thick pad. The top of the pad is 80 cm above the ground, and it compresses by $50 \mathrm{cm}$ as he comes to rest. What is his acceleration as he comes to rest on the pad?

Prabhat Tyagi

Numerade Educator

Problem 75

A Porsche challenges a Honda to a $400 \mathrm{m}$ race. Because the Porsche's acceleration of $3.5 \mathrm{m} / \mathrm{s}^{2}$ is larger than the Honda's $3.0 \mathrm{m} / \mathrm{s}^{2},$ the Honda gets a $100-\mathrm{m}$ head start $-$ it is only $300 \mathrm{m}$ from the finish line. Assume, somewhat unrealistically, that both cars can maintain these acceterations the entire distance. Who wins, and by how much time?

00000 00000

Numerade Educator

Problem 76

The minimum stopping distance for a car traveling at a speed of $30 \mathrm{m} / \mathrm{s}$ is $60 \mathrm{m},$ including the distance traveled during the driver's reaction time of 0.50 s.
a. Draw a position-versus-time graph for the motion of the car. Assume the car is at $x_{i}=0 \mathrm{m}$ when the driver first sees the emergency situation ahead that calls for a rapid halt.
b. What is the minimum stopping distance for the same car traveling at a speed of $40 \mathrm{m} / \mathrm{s} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 77

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rocket's acceleration?

Mayukh Banik

Numerade Educator

Problem 78

If an astronaut can jump straight up to a height of $0.50 \mathrm{m}$ on earth, how high could he jump on the moon?
A. $1.2 \mathrm{m}$
B. $3.0 \mathrm{m}$
C. $3.6 \mathrm{m}$
D. $18 \mathrm{m}$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 79

On the earth, an astronaut can safely jump to the ground from a height of $1.0 \mathrm{m} ;$ her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon?
$\mathrm{A}, 2.4 \mathrm{m}$
B. $6.0 \mathrm{m}$
C. $7.2 \mathrm{m}$
D. $36 \mathrm{m}$

00000 00000

Numerade Educator

Problem 80

On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of $3.0 \mathrm{s}$ before reaching the ground again. If a ball were to be thrown upward with the same initial speed on the moon, how much time would pass before it hit the ground?
A. $7.3 \mathrm{s}$
B. $18 \mathrm{s}$
C. $44 \mathrm{s}$
D. $108 \mathrm{s}$

Guilherme Barros

Guilherme Barros

Numerade Educator