AP Physics Set 1

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Rock X is released from rest at the top of a cliff that is on Earth. A short time later, Rock Y is released from rest from the same location as Rock X. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. After Rock Y is released from rest several seconds after Rock X is released from rest, what happens to the separation distance S between the rocks as they fall but before they reach the ground, and why? Take the positive direction to be downward.

A) Sis constant because at the moment Rock Y is released, the only difference between the rocks is their difference in height above the ground.
B)S is constant because the difference in speed between the two rocks stays constant as they fall.
C)S increases because the difference in speed between the two rocks increases as they fall.
D) S increases because at all times Rock X falls with a greater speed than Rock Y

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D) S increases because at all times Rock X falls with a greater speed than Rock Y

Correct. Rock X and Rock Y accelerate downward from the cliff toward Earth at the same rate, which means that both rocks gain their respective downward speeds at the same rate. This means that the numerical difference between their speeds remains the same as they fall toward Earth. However, at all times, Rock X will have a greater downward speed than Rock Y since Rock X has fallen for a greater interval of time. Therefore, between the time Rock Y is released and when it hits the ground, Rock X will have fallen a greater distance than Rock Y. Therefore, the separation distance between the rocks increases as they fall.

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An object is launched upward at angle θ0 above the horizontal with a speed of v0. The trajectory and three positions of the object, X, Y, and Z, are shown in the figure. Position X is higher than position Z with respect to the ground, and position Y is at the object's maximum vertical position. Which of the following claims is correct about the system that consists of only the object?

A) The speed of the object at position X is greater than the speed of the object at position Z.
B) The objects acceleration at point X is v0.
C) The object's acceleration is the same at position X, Y, and Z.
D)The object is at rest at position Y

C) The object's acceleration is the same at position X, Y, and Z.

Correct. At all points along the object's trajectory, the object's acceleration is the acceleration due to gravity that is always directed toward the center of Earth, or, in this case, toward the ground. The object does not accelerate in the horizontal direction at any point along the object's trajectory. Therefore, the object's acceleration remains the same at all points along the object's trajectory.

Toy car W travels across a horizontal surface with an acceleration of aw after starting from rest. Toy car Z travels across the same surface toward car W with an acceleration of az after starting from rest. Car W is separated from car Z by a distance d. Which of the following pairs of equations could be used to determine the location on the horizontal surface where the two cars will meet, and why?

A)x=x0+v0xt+1/2axt^2 for car W, and x=x0+v0xt+1/2axt^2 for car Z. Since the cars will meet at the same time, solving for t in one equation and placing the new expression for t into the other equation will eliminate all unknown variables except x.
B)x=x0+v0xt+1/2axt^2 for car W, and Δx=x−x0 for car Z. Since the separation distance is known between both cars, the displacement for car Z can be used in the equation for car W so that the time at which the cars meet can be determined. Once known, the time can be used to determine the meeting location.
C)Δx=x−x0 for car W, and x=x0+v0xt+1/2axt^2 for car Z. Since the separation distance is known between both cars, the displacement for car W
W can be used in the equation for car Z so that the time at which the cars meet can be determined. Once known, the time can be used to determine the meeting location.
D)Δx=x−x0 for car W, and Δx=x−x0 for car Z. Since the location at which the cars meet represents the final position of both cars, the separation distance for both cars can be substituted into both equations to determine the final position of both cars.

Correct. The following application of both equations may be used to determine the position at which the two cars meet.
For car W
x=x0+v0xt+1/2axt^2
x=(0+(0)t+1/2aWt^2
x=1/2aWt^2
t=√2x/aW
For car Z
x=x0+v0xt+1/2axt^2
x=d+(0)t−1/2aZt^2
x=d−12aZ(2x/aW)
x=d−aZ/aWx
x+aZ/aWx=d
x(1+aZ/aW)=d
x=d/1+aZaW

An object is held at an unknown height above Earth's surface, where the acceleration due to gravity of the object is considered to be constant. After the object is released from rest, a student must determine the object's speed the instant the object makes contact with the ground. Which of the following equations could the student use to determine the object's speed by using the fewest measuring tools if the student does not have access to a motion sensor? Select two answers.

A) vx=vx0+axt
B)x=x0+vx0t+1/2axt^2
C)v2x=v2x0+2ax(x−x0)
D)v¯=x−x0/t

A) vx=vx0+axt
C)v2x=v2x0+2ax(x−x0)

Correct. Without a motion sensor, the student would only need one stopwatch to use this equation to find the speed of the object at the instant it makes contact with the ground.

A ball traveling at a speed ν0 rolls off a desk and lands at a horizontal distance x0 away from the desk, as shown in the figure. The ball is then rolled off of the same desk at a speed of 3 v0. At what horizontal distance will the ball land from the table?

A)x0
B)3x0
C)6x0
D)9x0

B)3x0

Correct. The horizontal distance can be determined by applying the following kinematic equation: x=x0+v0xt+1/2axt^2. In both situations, the initial position of the ball can be considered as zero, and the ball does not experience a horizontal acceleration. Since the ball's height above the ground remains constant in both situations, the time it takes for the ball to hit the ground will be the same in both situations. Therefore, the following relationship can be concluded: x~v0x. Therefore, if the initial speed of the ball is increased by a factor of 3, then the horizontal distance traveled by the ball should be increased by a factor of 3.