Chapter 2 AP Physics

As a freely falling object speeds up, what is happening to its acceleration - does it increase, decrease, or stay the same? (a) Ignore air resistance. (b) Consider air resistance.

(a) If air resistance can be ignored, the acceleration of a freely falling object is constant. As we will learn in chapter 4, acceleration is caused by a net, unbalanced force acting on an object. If gravity is the only force acting on the object, and if the gravitational force on an object is constant at the surface of Earth, then the acceleration of freely falling objects must be constant. (b) The object is no longer in free fall and the net force stays at 0.

A rock is dropped off a cliff that's 80 m high. If it strikers the ground with an impact velocity of 40 m/s, what acceleration did it experience during its descent?

10 m/s^2

Traveling along a single axis, a car starts 10 m from the origin. The car then moves 8 m directly away from the origin and then turns around and moves 12 m back toward the origin. Determine the final position of the car, the distance the car traveled and the displacement of the car.

-4 m

Spotting a police car ahead, the driver of the car in the previous example slows from 32 m/s to 20 m/s in 2 seconds. Find the car's average acceleration.

-6 m/s

A car is traveling in a straight line along a highway at a constant speed of 80 mph for 10 seconds. Find its acceleration.

0

In a track-and-field event, an athlete runs exactly once around an oval track, a total distance of 500 m. Find the runner's displacement of the race.

0

If the infant on the 2nd question completes his journey in 20 seonds, find the magnitude of his average velocity.

0.34 m/s

Does the odometer in a car measure distance or displacement?

Distance

When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path?

v = 0, but a ≠ 0

You throw a ball upward with an intial speed of 10 m/s. Assuming there is no air resistance, what is its speed when it returns to you?

10 m/s

A baseball is thrown straight upward with an initial speed of 20 m/s. How high will it go?

20 m

An object with an initial velocity of 4 m/s moves along a straight axis under constant acceleration. Three seconds later, its velocity is 14 m/s. How far did it travel during this time?

27 m

You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.) Screenshot in desktop (Named 2.15a)

3, the ball is going downwards so the graph should be going down all the time.

You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this motion? Screenshot in desktop (Named 2.15c) LOOK AT 2.15D AFTER

4

You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph for this motion? (Assume your y-axis is pointing up.) Screenshot in desktop (Named 2.15b)

4

A car is traveling along a straight highway at a speed of 20 m/s. The driver steps on the gas pedal and, 3 seconds later, the car's speed is 32 m/s. Find its average acceleration.

4 m/s^2

A rock is dropped from an 80-meter cliff. How long does it take to reach the ground?

4 s

One second after being thrown straight down, an object is falling with a speed of 20 m/s. How fast will it be falling 2 seconds after it was traveling 20 m/s?

40 m/s

A car initially traveling at 10 m/s accelerates uniformly for 4 seconds at a rate of 2 m/s^2, in a straight line. How far does the car travel during this time?

56 m

An infant crawls 5 m east, then 3 m north, then 1 m east. Find the magnitude of the infant's displacement.

6.7 m

Which of these motions is not at constant acceleration: a rock falling from a cliff, an elevator moving from the second floor to the fifth floor making stops along the way, a dish resting on a table? Explain your answers.

A rock falling from a cliff has constant acceleration if air resistance can be ignored, but the magnitude of the acceleration decreases if air resistance is present. An elevator moving from the second floor to the fifth floor making stops along the way does not have constant acceleration because, as it moves up, sometimes it is speeding up. A dish resting on a table has a constant acceleration of zero. The dish has no acceleration because it is not speeding up or slowing down.

A ball is thrown straight upward with some initial speed. When it reaches the top of its flight (at a height h), a second ball is thrown straight upward with the same intial speed. Where will the balls cross paths?

Above height h/2

Assume that the runner in the 3rd question completes the race in 1 minute and 18 seconds. Find her average speed and the magnitude of her average velocity.

Average Speed = 6.4 m/s Average velocity = 0 m/s

Describe in words the motion plotted in this graph. Use terms like position, velocity, and acceleration.

Between 0 and 20 s, the object's position changes at a constant rate. Velocity is the slope of a position-time graph. Thus the object has constant, positive velocity from 0 to 20 s. The slope of the graph increases from 20 s to about 30 s. The velocity changes (increased), so the acceleration was positive during this time. From 30 to 35 s, the slope of the graph decreases, so the object is slowing down, and the acceleration is negative. From 35-50 s, the object is losing position, so the velocity becomes negative. Also, the slope of the graph is becoming steeper (up to about 42 s), so the acceleration is negative. After around 42 s, the slope is becoming less negative, so the acceleration is positive.

You drop a rock off a bridg.e When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their velocities?

Both increase at the same rate

Can the velocity of an object be negative when its acceleration is positive? What about vice versa? If yes, give examples in each case.

Both yes. For example, an object can have a velocity of −10 𝑚/𝑠 and an acceleration of +1 𝑚/𝑠2. That means that, each second, the object's velocity becomes less negative. So it is slowing down as it moves in the negative direction. An example of the opposite case is an object moving at +10 m/s and accelerating at −1 𝑚/𝑠2. Each second, its speed is becoming less negative, so that it is slowing down as it moves in the positive direction.

Consider the line labeled B in the v versus t plot. How does the speed change with time for line B? Screenshot in desktop (Named 2.14b)

Decreases, then increases

You drive for 30 minutes at 30 mi/hr and then another 30 minutes at 50 mi/hr. What is your average speed for the whole trip.

Equal to 40 mi/hr

Give an example where both the velocity and acceleration are negative.

If you threw an object downwards, the velocity and acceleration would be negative.

Consider the line labeled A in the v versus t plot. How does the speed change with time for line A? Screenshot in desktop (Named 2.14a)

Increases

The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? Screenshot in desktop (Named 2.13a)

It moves at constant velocity

The graph of position vs. time for a car is given below. What can you say about the velocity of the car over time? Screenshot in desktop (Named 2.13b)

It slows down all the time

You throw a ball striahgt up into the air. After it leaves your hand, at what point in its flight does it have the maimum value of acceleration?

Its acceleration is constant everywhere

You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/her. What is your average speed for the whole 8-mile trip?

Less than 40 mi/hr

Alice and Bill are at the top of a building. Alice throws her ball downward. Bill simply dorps his ball. Which ball has greater acceleration just after release?

Neither, they both have the same acceleration

Does the displacement of an object depend on the specific location of the origin of the coordinate system?

No

If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval?

No

If the position of a car is zero, does its speed have to be zero?

No

If one object has a greater speed than a second object, does the first necessarily have a greater acceleration? Explain, using examples.

No, an object can be moving slower than another one, but its acceleration can be much greater than the faster-moving object. If the velocity is constant for the 1st object, and the 2nd object increases in velocity the 2nd object has a higher acceleration.

STUDY THE CALCULUS QUESTIONS

ON THE PRINCETON WORKSHEET

Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with the acceleration of a bicycle that accelerates from rest to 10 km/h in the same time.

Same acceleration. The definition of acceleration is (change in speed) / (time). The motorcycle's change in speed is (90 km/h - 80 km/h) = 10 km/h. the bicycle's change in speed is (10 km/h - 0 km/h) = 10 km/h. Both have the same change in speed, and the amount of time required to change speed is the same for both. Since the numerator and denominator in the calculation of acceleration are the same, the result of the division is the same.

Does a car speedometer measure speed, velocity, or both?

Speed

Does the speedometer in a car measure velocity or speed?

Speed

You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall,w hat happens to their separation?

The separation increases as they fall

Describe in words the motion plotted in this graph. Use terms like position, velocity, and acceleration.

The velocity increases at a constant rate from 0 to 50 s. The slope of a velocity-time graph is acceleration, so the acceleration is constant and positive. At about 50 s, the slope becomes zero, so the acceleration is zero. Between 50- 90 s, the velocity decreases, so the object is slowing down. The slope is negative, so the acceleration is negative. Between 90 to about 108 s, the velocity is zero, and the object is at rest. From 108 s to 125 s, the object's velocity increases, and it begins to speed up. The slope is positive, so the acceleration is positive.

Alice and Bill are at the top of a cliff of height H. Both throw a ball with initial speed, Alice straight down and Bill straight up. The speeds of the balls when they hit the ground are Va and Vb. If there is no air resistance, which is true?

Va=Vb

A baseball player hits a ball straight up into the air. It leaves the bat with a speed of 120 km/h. In the absence of air resistance, how fast would the ball be traveling when it is caught at the same height above the ground as it left the bat? Explain.

When the ball comes back down, it has exactly the same speed, but travels in the opposite direction. As the ball travels up, it slows down because of the acceleration due to gravity. Each second, the ball slows down by 9.8 m/s, or 35.3 km/h each second. After one second, the ball's speed is (120 km/h - 35.3 km/h) = 84.7 km/h. In the next second, it loses another 35.3 km/h, and its speed becomes 49.4 km/h. After three seconds, the speed is 14.1 km/h. The speed reaches zero in (14.1 / 35.3) s = 0.4 s. Thus the ball comes to rest after 3.4 s. On its way down, it gains 35.3 km/h of speed each second. After 3.4 s, its speed is 120 km/h.

If the velocity of a car is non-zero, can the acceleration of the car be zero?

Yes

You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement?

Yes

Is it possible to move with constant speed but not constant velocity? Is it possible to move with constant velocity but not constant speed?

Yes, No

Can an object have zero velocity and nonzero acceleration at the same time? Give examples.

Yes. For example, the instant you let go of something and it begins to fall, the velocity is zero, but the acceleration due to gravity is 9.8 m/s2 downward.

Can an object have a northward velocity and a southward acceleration? Explain.

Yes. It could be facing north with its velocity and south with its acceleration. With them facing the opposite directions, it is constantly slowing down.

Can an object have zero acceleration and nonzero velocity at the same time? Give examples.

Yes. When a car is moving with no change in velocity, the acceleration is zero.