Review

Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible.

Which of the following graphs correctly shows the vertical velocity of rock XX as a function of time? Take the positive direction to be upward.

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Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible.

Which of the following graphs best represents the vertical displacement of Rock XX as a function of time starting from immediately after the rock is released from rest? Take the positive direction to be downward.

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Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible.

After Rock YY is released from rest several seconds after Rock XX is released from rest, what happens to the separation distance SS between the rocks as they fall but before they reach the ground, and why? Take the positive direction to be downward.

• SS is constant because at the moment Rock YY is released, the only difference between the rocks is their difference in height above the ground.

• SS is constant because the difference in speed between the two rocks stays constant as they fall.

• SS increases because the difference in speed between the two rocks increases as they fall.

• SS increases because at all times Rock XX falls with a greater speed than Rock YY.

An object travels along a straight, horizontal surface with an initial speed of 2 ms2 ms. The velocity of the object as a function of time is given in the table above. Which of the following graphs represents the object’s acceleration as a function of time?

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Two objects, object X and object Y, are held together by a light string and are released from rest near a planet’s surface in the orientation that is shown in the figure. Object X has a greater mass than object Y. A graph of the acceleration as a function of time for the system’s center of mass is shown for the 4s. The positive direction is considered to be upward. How does the speed of object X vx compare to that of the system’s speed vs after the objects have fallen for 4s?

• vx=vs

• vx>vs

• vx<vs

• The answer cannot be determined without knowing the relative masses of object XX and object YY.

A student uses a motion sensor to collect data of the velocity of an object as a function of time during two experimental trials, as shown. In which trial does the object have the greatest magnitude of acceleration(GMA), and in which trial does the object travel the greatest distance(D)?

• GMA: Trial 1

  D: Trial 1

• GMA: Trial 2

  D: Trial 2

• GMA: Trial 1

  D: Trial 2

• GMA: Trial 2

  D: Trial 1

Car XX and car YY travel on a horizontal surface along different parallel, straight paths. Each car’s velocity as a function of time is shown in the graph. Which of the following claims is correct about car XX and car YY?

• Both car XX and car YY travel in the same direction.

• Between t=6 st=6 s and t=7 st=7 s, car XX and car YY are at the same horizontal position.

• The change in car XX’s speed per unit of time increases as the time increases, and the change in car YY’s speed per unit of time decreases as the time increases.

• The magnitude of the acceleration of car XX is the same as the magnitude of the acceleration of car YY.

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

• The speed of the object at position XX is greater than the speed of the object at position ZZ.

• The object’s speed at point ZZ is v0

• The object’s acceleration is the same at positions XX, YY, and ZZ.

• The object is at rest at position YY.

Answer explanation

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.

The table shows the vertical position as a function of time for an object that is dropped from a height of 5 m5 m. A student must determine the acceleration of the object. Which of the following procedures could the student use to make the determination? Justify your selections. Select two answers.

• Create a graph of yy as a function of t2t2, since the slope will be equal to the acceleration due to gravity.

• Use vy=Δy/Δtv to determine the average vertical speed of the ball, and then divide the average speed by the time in which the ball was in the air, since the average speed and time interval is used to determine an object’s acceleration.

• Use y=y0+vy0t+12ayt2, since all quantities are known except for the acceleration due to gravity.

• Create a position-versus-time graph of the ball’s motion, and use the data to create a velocity-versus-time graph of the ball’s motion, since the slope of the velocity-versus-time graph represents the acceleration.

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.

• vx=vx0+axt

• x=x0+vx0t+(1/2)axt^2

• v2x=v2x0+2ax(x−x0)

• v¯=x−x0t