Chapter Questions
As you read this in your chair, how fast are you moving relative to the chair? Relative to the Sun?
Differentiate between average speed and instantaneous speed.
What kind of speed is registered by an automobile speedometer: average speed or instantaneous speed?
What is the average speed in kilometers per hour of a car that covers a distance of 10 km in 10 minutes?
How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min?
Why is velocity a vector quantity?
Can an object moving with a constant velocity move in a curved path?
If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, does it maintain a constant speed? A constant velocity? Defend your answers.
A car’s velocity increases from 40 to 50 km/h in 10 s. What is its acceleration?
What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s? (Why do some of your classmates who correctly answer the preceding question get this question wrong?)
When are you most aware of your motion in a moving vehicle: when it is moving steadily in a straight line or when it is accelerating? If you were in a car that moved with absolutely constant velocity (no bumps at all), would you be aware of motion?
Acceleration is generally defined as the time rate of change of velocity. When can it be defined as the time rate of change of speed?
What did Galileo discover about the amount of speed a ball gained each second when rolling down an inclined plane? What did this say about the ball’s acceleration?
What is the relationship between velocity and acceleration? If the acceleration of a ball is 3 $\mathrm{m} / \mathrm{s}^{2}$ , what is its velocity 2 seconds after starting from rest?
Does a freely falling body have uniform velocity?
What is the relationship between instantaneous velocity and $g$ for a freely falling body?
What is the speed acquired by a freely falling object 2 s after being dropped from a rest position? Will your answer change if the object was not at rest?
The acceleration of free fall is about 10 $\mathrm{m} / \mathrm{s}^{2}$ . Why does the sconds unit appear twice?
What is the direction of acceleration for a body thrown upwards?
What is the relationship between distance travelled and time for a uniformly accelerated body?
What is the distance fallen for a freely falling object 1s after being dropped from a rest position? What is the distance for a 4-s drop?
How does friction affect the free fall of an object?
Consider these measurements: $10 \mathrm{m}, 10 \mathrm{m} / \mathrm{s},$ and 10 $\mathrm{m} / \mathrm{s}^{2}$ Which is a measure of speed, which of distance, and which of acceleration?
What is the speed over the ground of an airplane flying at 200 km/h relative to the air caught in a 100 km/h right–angle crosswind?
Your grandfather is interested in your educational progress. Without using equations explain to him the difference between velocity and speed.
Try this with your friends. Hold a dollar bill so that the midpoint hangs between a friend’s fingers and challenge him to catch it by snapping his fingers shut when you release it. He won’t be able to catch it! Explanation: From $d=1 / 2 g t^{2}$ the bill will fall a distance of 8 centimeters (half the length of the bill) in a time of $1 / 8 \mathrm{sec}-$ ond, but the time required for the necessary impulses to travel from his eye to his brain to his fingers is at least 1$/ 7$ second.
You can compare your reaction time with that of a friend by catching a ruler that is dropped between your fingers. Let a friend hold the ruler as shown and you snap your fingers as soon as you see the ruler released. The number of centimeters that pass through your fingers depends on your reaction time. You can express the result in fractions of a second by rearranging $d=1 / 2 g t^{2}$ . Expressed for time, it is $t=\sqrt{2} d l g=0.045 \sqrt{d}$ where $d$ is in centimeters.
Stand flat-footed next to a wall. Make a mark on the wall at the highest point you can reach. Then jump vertically and mark this highest point. The distance between the two marks is your vertical jumping distance. Use these data to calculate your personal hang time.
Show that the average speed of a tortoise that covers a distance of 10 cm in 10 s is 0.01 m/s.
Calculate your average walking speed when you step 1.0 m in 0.5 s.
Show that the acceleration of a car that can go from rest to 100 km/h in 10 s is 10 km/h·s.
Show that the acceleration of a hamster is 5 $\mathrm{m} / \mathrm{s}^{2}$ when it increases its velocity from rest to 10 $\mathrm{m} / \mathrm{s}$ in 2 $\mathrm{s}$ .Distance $=$ average speed $\times$ time
Show that the hamster in the preceding problem travels a distance of 22.5 m in 3 s.
Show that a freely falling rock drops a distance of 20 m when it falls from rest for 2 s.
You toss a ball straight up with an initial speed of 20 m/s. How much time does it take to reach its maximum height (ignoring air resistance)?
A ball is tossed with enough speed straight up so that it is in the air several seconds. (a) What is the velocity of the ball when it reaches its highest point? (b) What is its velocity 1 s before it reaches its highest point? (c) What is the change in its velocity during this 1-s interval? (d) What is its velocity 1 s after it reaches its highest point? (e) What is the change in velocity during this 1-s interval? (f) What is the change in velocity during the 2-s interval? (Careful!) (g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?
What is the instantaneous velocity of a freely falling object 10 s after it is released from a position of rest? What is its average velocity during this 10-s interval? How far will it fall during this time?
A car takes 10 s to go from $v=0 \mathrm{m} / \mathrm{s}$ to $v=25 \mathrm{m} / \mathrm{s}$ at constant acceleration. If you wish to find the distance traveled using the equation $d=1 / 2 a t^{2},$ what value should you use for $a$ ?
Surprisingly, very few athletes can jump more than 2 feet $(0.6 \mathrm{m})$ straight up. Use $d=1 / 2 g t^{2}$ to solve for the time one spends moving upward in a $0.6-\mathrm{m}$ vertical jump. Then double it for the "hang time " - the time one's feet are off the ground.
A dart leaves the barrel of a blowgun at a speed $v$ . The length of the blowgun barrel is $L$ . Assume that the acceleration of the dart in the barrel is uniform.a. Show that the dart moves inside the barrel for a time of 2$L / v .$b. If the dart's exit speed is 15.0 $\mathrm{m} / \mathrm{s}$ and the length of the blowgun is $1.4 \mathrm{m},$ show that the time the dart is in the barrel is 0.19 s.
Jogging Jake runs along a train flatcar that moves at the velocities shown in positions A–D. From greatest to least, rank Jake’s velocities relative to a stationary observer on the ground. (Call the direction to the right positive.)
A track is made from a piece of channel iron as shown. A ball released at the left end of the track continues past the various points. Rank the speeds of the ball at points A, B, C, and D, from fastest to slowest. (Watch for tie scores.)
A ball is released at the left end of three different tracks. The tracks are bent from equal-length pieces of channel iron.a. From fastest to slowest, rank the speeds of the balls at the right ends of the tracks.b. From longest to shortest, rank the tracks in terms of the times for the balls to reach the ends.c. From greatest to least, rank the tracks in terms of the average speeds of the balls. Or do all the balls have the same average speed on all three tracks?
Three balls of different masses are thrown straight upward with initial speeds as indicated.a. From fastest to slowest, rank the speeds of the balls 1 s after being thrown.b. From greatest to least, rank the accelerations of the balls 1 s after being thrown. (Or are the accelerations the same?)
Here we see a top view of an airplane being blown off course by winds in three different directions. Use a pencil and the parallelogram rule to sketch the vectors that show the resulting velocities for each case. Rank the speeds of the airplane across the ground from fastest to slowest.
Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least fora. the time to reach the opposite shore.b. the fastest ride.
Mo measures his reaction time to be 0.18 s in Think and Do Exercise 27. Jo measures her reaction time to be 0.20 s. Who has the more favorable reaction time? Explain.
Jo, with a reaction time of 0.2 second, rides her bike at a speed of 6.0 m/s. She encounters an emergency situation and “immediately” applies her brakes. How far does Jo travel before she actually applies the brakes?
What is the impact speed of a car moving at 100 km/h that bumps into the rear of another car traveling in the same direction at 98 km/h?
Suzie Surefoot can paddle a canoe in still water at 8 km/h. How successful will she be canoeing upstream in a river that flows at 8 km/h?
Is a fine for speeding based on one’s average speed or instantaneous speed? Explain.
One airplane travels due north at 300 km/h while another travels due south at 300 km/h. Are their speeds the same? Are their velocities the same? Explain.
Light travels in a straight line at a constant speed of 300,000 km/s. What is the acceleration of light?
You’re traveling in a car at some specified speed limit. You see a car moving at the same speed coming toward you. How fast is the car approaching you, compared with the speed limit?
You are driving north on a highway. Then, without chang- ing speed, you round a curve and drive east. (a) Does your velocity change? (b) Do you accelerate? Explain.
Jacob says acceleration is how fast you go. Emily says acceleration is how fast you get fast. They look to you for confirmation. Who’s correct?
Starting from rest, one car accelerates to a speed of 50 km/h, and another car accelerates to a speed of 60 km/h. Can you say which car underwent the greater acceleration? Why or why not?
What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 s? Explain your answer.
Which is greater: an acceleration from 25 km/h to 30 km/h or from 96 km/h to 100 km/h, both occurring during the same time?
Galileo experimented with balls rolling on inclined planes of various angles. What is the range of accelerations from angles $0^{\circ}$ to $90^{\circ}$ (from what acceleration to what)?
Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its reading in speed increase with each second of fall?
Suppose that the freely falling object in the preceding exercise were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds?
For a freely falling object dropped from rest, what is the acceleration at the end of the fifth second of fall? Tenth second of fall? Defend your answers.
If air resistance can be ignored, how does the acceleration of a ball that has been tossed straight upward compare with its acceleration if simply dropped?
When a ballplayer throws a ball straight up, by how much does the speed of the ball decrease each second while ascending? In the absence of air resistance, by how much does the speed increase each second while descending? What is the time required for rising compared to falling?
Boy Bob stands at the edge of a cliff (as in Figure 3.8) and throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below?
Answer the preceding question for the case where air resistance is not negligible—where air drag affects motion.
While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?
Consider a vertically launched projectile when air drag is negligible. When is the acceleration due to gravity greatest: when ascending, at the top, or when descending Defend your answer.
Extend Tables 3.2 and 3.3 to include times of fall of 6 to 10 s, assuming no air resistance.
If there were no air resistance, why would it be dangerous to go outdoors on rainy days?
For an object in free fall, how does acceleration vary with the distance traveled?
A ball tossed upward will return to the same point with the same initial speed when air resistance is negligible. When air resistance is not negligible, how does the return speed compare with its initial speed?
Why would a person’s hang time be considerably greater on the Moon than on Earth?
Why does a stream of water get narrower as it falls from a faucet?
Vertically falling rain makes slanted streaks on the side windows of a moving automobile. If the streaks make an angle of $45^{\circ}$ , how does the speed of the automobile compare with the speed of the falling rain?
Make up a multiple-choice question that would check a classmate’s understanding of the distinction between speed and velocity.
Make up a multiple-choice question that would check a classmate’s understanding of the distinction between velocity and acceleration.
Can an automobile with a velocity toward the north simultaneously have an acceleration toward the south? Convince your classmates of your answer.
Can an object reverse its direction of travel while main- taining a constant acceleration? If so, cite an example to your classmates. If not, provide an explanation.
For straight-line motion, explain to your classmates how a speedometer indicates whether or not acceleration is occurring.
Correct your friend who says, “The dragster rounded the curve at a constant velocity of 100 km/h.”
Cite an example of something with a constant speed that also has a varying velocity. Can you cite an example of something with a constant velocity and a varying speed? Defend your answers.
Cite an instance in which your speed could be zero while your acceleration is nonzero.
Cite an example of something that undergoes acceleration while moving at constant speed. Can you also give an example of something that accelerates while traveling at constant velocity? Explain to your classmates.
(a) Can an object be moving when its acceleration is zero? If so, give an example. (b) Can an object be accelerating when its speed is zero? If so, give an example.
Can you cite an example in which the acceleration of a body is opposite in direction to its velocity? If so, what example can you cite to your classmates?
On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.)
Suppose that the three balls shown in Exercise 88 start simultaneously from the tops of the hills. Which one reaches the bottom first? Explain.
Be picky and correct your friend who says, “In free fall, air resistance is more effective in slowing a feather than a coin.”
If you drop an object, its acceleration toward the ground is 10 $\mathrm{m} / \mathrm{s}^{2}$ . If you throw it down instead, would its acceleration after throwing be greater than 10 $\mathrm{m} / \mathrm{s}^{2}$ ? Why or why not?
In the preceding exercise, can you think of a reason why the acceleration of the object thrown downward through the air might be appreciably less than 10 $\mathrm{m} / \mathrm{s}^{2} ?$ Discuss your reason with your classmates.
A friend says that if a car is traveling toward the east, it cannot at the same time accelerate toward the west. What is your response?
Madison tosses a ball straight upward. Anthony drops a ball. Your discussion partner says both balls undergo the same acceleration. What is your response?
Two balls are released simultaneously from rest at the left end of equal-length tracks A and B as shown. Which ball reaches the end of its track first?
Refer to the pair of tracks in the preceding exercise. (a) On which track is the average speed greater? (b) Why are the speeds of the balls at the ends of the tracks the same?
A rowboat heads directly across a river at a speed of 3 m/s. Convince your classmates that if the river flows at 4 m/s, the speed of the boat relative to the riverbank is 5 m/s.
If raindrops fall vertically at a speed of 3 m/s and you are running horizontally at 4 m/s, convince your classmates that the drops will hit your face at a speed of 5 m/s.
An airplane with an airspeed of 120 km/h encounters a 90-km/h crosswind. Convince your classmates that the plane’s groundspeed is 150 km/h.
In this chapter, we studied idealized cases of balls rolling down smooth planes and objects falling with no air resistance. Suppose a classmate complains that all this attention focused on idealized cases is worthless because idealized cases simply don’t occur in the everyday world. How would you respond to this complaint? How do you suppose the author of this book would respond?