Physics Chapter 3
9. What is the acceleration of a car moving along a staight road that increases its speed from 0 to 100 km/h in 10 seconds?
10 km/h/s
15. What exactly is meant by a "freely falling" object?
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18. The acceleration of free fall is about 10 m/s². Why does the seconds unit appear twice?
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71. If there were no air resistance, why would it be dangerous to go outdoors on rainy days?
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72. As speed increases for an object in free fall, does acceleration increase also?
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2. What two units of measurements are necessary for describing speed?
Distance traveled Time of travel.
22. What is the effect of air resistance on the acceleration of falling objects?
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76. Vertically falling rain makes slanted streaks on the side windows of a moving car. If the streaks make an angle of 45⁰, how does the speed of the car compare with the speed of the falling rain?
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39. Surprisingly, very few athletes can jump more than 2 feet (0.6 m) straight up. Use d = ½gt² to solve for the time one spends moving upward in a 0.6 m vertical jump. Then double it for the "hang time" the time one's feet are off the ground.
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52. One airplane travels due north at 300km/h while another travels due south at 300km/h. Are their speeds the same? Are their velocites the same? Explain
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62. 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?
Distance reading would indicate greater distances fallen in successive seconds. During each successive second the object falls faster and covers greater distance.
26. Hold a dollar bill so that the midpoint hangs between your fingers and challenge them to catch it by snapping his fingers shut when you release it. He won't be able to catch it.
From d=½ gt², the bill will fall a distance of 8 centimeters (half the length of the bill) in a time of 1/8 second, but the time required for the necessary impulses to travel from his eye to his brain to his fingers is at least 1/7 seconds.
28. 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 this data to calculate your personal hang time.
Hang times won't exceed 1 second
8. 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
No, it changed direction
66. Boy Bob stands on the edge of a cliff and throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resitance is negligible, which ball will have the greater speed when it strikes the ground below?
They will strike at the same time at the same speed
25. Grandma is interested in your educational progress. Text Grandma and, without using equations, explain to her the difference between velocity and acceleration.
Velocity is how fast you are traveling and acceleration is how quickly your speed changes.
12. Acceleration is generally defined as the time rate of change in velocity. When can it be defined as the time rate of change of speed?
When motion is in one direction along a straight line, either can be used.
7. If a car moves with a constant velocity, does it also move with a constant speed?
Yes
51. Is a fine for speeding based on one's average speed or instantaneous speed? Explain
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29. Show that the average speed of a rabbit that runs a distance of 30 m in a time of 2 s is 15 m/s. Speed + distance/time
30m/2s = 15m/s
3. What kind of speed is registered by an automobile speedometer: average or instantaneous
instantaneous
13. What did Galileo discover about the amount of speed a ball gained each second when rolling down and inclined plane? What did this say about the ball's acceleration?
the ball gained the same amount of speed each second, which says the acceleration is constant
54. 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?
twice the speed limit
19. When an object is thrown upward, how much speed does it lose each second?
10 m/s for each second moving upward.
5. How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min?
12.5 km
21. What is the distance fallen for a freely falling object 1 second after being dropped from a rest position? What is the distance for a 4 second drop?
5 m and 80 m
10. What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 seconds?
Zero, because the velocity does not change
65. 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?
the time rising equals the time falling
41. Jogging Jake runs along a train that moves at the velocities shown below. From greatest to least, rank Jake's velocities relative to stationary observer on the ground. (call the direction to the right positive) a) 4m/s← →8m/s b) 6m/s→ ←10m/s c) 4m/s→ →6m/s d) 6m/s← →18m/s
d,c,a,b
30. Calculate your average walking speed when you step 1.0 m in 0.5 s. Speed + distance/time
1.0m/0.5s = 2m/s
31. Show that the acceleration of a car that can go from rest to 100 km/h in 10 s is 10 km/h s. Average Speed = Total Distance Coveres/Time Interval
100km/h ÷ 10s = 10km/h s
32. Show that the acceleration of a hamster is 5 m/s² when it increases its velocity from rest to 10 m/s in 2 s. Average Speed = Total Distance Coveres/Time Interval
10m/s ÷ 2s = 5m/s²
49. What is the impact speed of a car moving at 100km/h that bumps into the rear of another car traveling in the same direction at 98km/h?
2km/h 100 - 98 =
57. Starting from rest, one car accelerates to a speed of 50km/h, and another to 60km/h. Can you say which car underwent the greater acceleration? Why/Why not
No, unless you know the time involved.
50. Suzie can paddle a canoe in still water at 8km/h. How successful will she be canoeing upstream in a river that flows 8km/h?
her velocity would be zero 8 - 8
75. Why does a stream of water get narrower as it falls from a faucet?
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61. 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?
10 m/s each second
33. Show that the hamster in the preceeding problem travels a distance of 22.5 m in 3 s. Distance = Average Speed x Time
22.5m = ½ (5m/s²) (3s)²
1. As you read this in your chair, how fast are you moving relative to the chair? Relative to the sun?
Relative to the chair your speed is zero. Relative to the sun it is 30 km/s.
67. Answer the preceding question for the case where air resistance is not negligible -- where air drag affects motion.
The ball thrown down would have the greater speed.
68. 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?
counting time means twice the time. In twice the time the ball will roll 4x as far.
45. 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 slower.
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46. Here we see top views of three boats crossing a river. All have the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least for: a) the time to reach the opposite shore b) the fastest ride
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16. What is the gain in speed per second for a free falling object?
10 m/s each second
63. 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
g = 10m/s the velocity would be different but not the acceleration
73. 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?
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74. Why would a person's hang time be considerably greater on the moon than on earth?
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23. Consider these measurements: 10m, 10 m/s, and 10 m/s². Which is a measure of speed, which of distance, and which of accerleration?
10 m/s = speed 10m = distance 10m/s²= acceleration
4. What is the average speed in kilometers per hour of a horse that gallops a distance of 15 km in a time of 30 min?
30 km/hr
17. What is the speed acquired by a freely falling object 5 seconds after being dropped from a rest position? What is the speed 6 second after?
50 m/s and 60 m/s
27. 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 ou 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 second by rearranging d=½ gt². Expressed for time, it is t=√2 dlg = 0.045 √d, where d is in centimeters.
20. What relationship between distance traveled and time did Galileo discover for freely falling objects released at rest?
distance traveled is directly proportional to the square of the time of travel. (d=½gf²)
59. Which is greater: an acceleration from 25km/h to 30kmh or from 96km/h to 100km/h, both occuring during the same time?
from 25 to 30
64. 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?
g = 10m/s
58. What is the acceleration of a car that moves at a steady velocity of 100km/h for 100s? Explain
zero
38. A car takes 10 s to go from v = 0 m/s to v = 25 m/s at consant acceleration. If you wish to find the distance traveled using the equation d = ½at², what value should you use for d?
25m/s-0 ÷ 10s = 2.5 m/s²
34. Show that a freely falling rock drops a distance of 45 m when it falls from rest for 3 s. Distance = Average Speed x Time
45m = ½ (10ms²) (3s)²...
11. 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 absolutley constant velocity, would you be aware of motion?
Accelerating
60. Galileo experimented with balls rolling on inclined planes of various angles. What is the range of acceleration from angles 0⁰ to 90⁰ (from what acceleration to what)?
At 0⁰ the acceleration is zero. At 90⁰ the acceleration is that of free fall, g. So the range of accelerations is 0 to 10 m/s²
53. Light travels in a straight line at a constant speed of 300,000km/s. What is the acceleration of light?
There is no acceleration
47. Mo measures his reaction time to be 0.18 s in ex. 27. Jo measures her reaction time to be 0.20 s. Who has the more favorable reaction time. Explain
Mo
35. You toss a ball straight up with an initial speed of 30 m/s. How high does it go, and how long is it in the air?
Since it starts up at 30m/s and loses 10m/s each second, its time going up is 3 seconds and time going down is 3 seconds. The ball is in the air a total of 6 seconds. d=½gt² ½ 5 × 3² = 45m
6. What is the main difference between speed and velocity?
Speed is a scalar while velocity is a vector
40. 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 2L/v b) If the dart's exit speed is 15.0 m/s and the length of the blowgun is 1.4 m, show that the time the dart is in the barrel is 0.19 s.
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42. 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)
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43. 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 term 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. Of do all the balls have the same average speed on all three tracks?
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56. Jacob says acceleration is how fast you go. Emily says acceleration is how fast you get fast. They look to you for confirmation. Who is correct?
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70. Extend tables 3.2 and 3.2 to include times of fall of 6 to 10 s, assuming no air resistance.
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24. What is the speed over the ground of an airplane flying at 100 km/h reltaive to the air caught in a 100 km/h right angle crosswind?
The resultant is 141km/h at an angle of 45⁰ to the plane's intended direction of travel.
44. Three balls of different masses are thrown straight upward with initial speeds as indicated. a) 10m/s ↑1.0kg b) 15m/s ↑1.5 kg c) 3m/s ↑ 0.8kg 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 is the acceleration the same)
a) c,b,a b) acceleration would be = (10 m/s²)
36. 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? g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?
a) zero b) 10 m/s c) 10 m/s d) -10 m/s e) 10 m/s f) 20 m/s g) 10 m/s²
14. What relationship did Galileo discover about a ball's acceleration and the steepness of an incline? What acceleration occurs when the plane is vertical?
if vertical, the acceleration is that of free fall
69. 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
stays at a constant
55. You are driving north on a highway. Then, without changing speed, you round a curve and drive east. a) Does your velocity change? b) Do you accelerate?
yes yes
77. Make up a multiple choice question that would check a classmate's understanding of the distinction between speed and velocity.
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78. Make up a multiple choice question that would check a classmate's understanding of the distinciton between veocity and acceleration.
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48. Jo, with a reaction time 0.2 s, 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?
1.2m 6.0 × 0.2 =
37. What is the instantaneous velocity of a freely falling object 10 s after it is released from a poisition of rest? What is its average velocity during this 10 s interval? How far will it fall during this time?
10 m/s² × 10s = 100 m/s 50 m/s velocity 500 m distance
