Representing Motion (College Board AP® Physics 1: Algebra-Based): Exam Questions

A ball is dropped from rest from a height of above the ground. Air resistance is present. 

Using kinematic equations, derive an expression for the velocity of the ball just before it hits the ground and state any assumptions made.

On the axis provided in Figure 2 sketch a velocity-time graph of the motion of the ball from the point of release to when it hits the ground.

Figure 2

On the axis provided in Figure 3 sketch a displacement-time graph of the motion of the ball from the point of release to the point just before it hits the ground.

Figure 3

A group of students want to determine the acceleration due to gravity by analyzing the motion of a freely falling object. They have access to standard laboratory equipment plus the following:

• a ball bearing

• an electromagnet

Describe an experimental procedure the students could use to collect the data necessary to determine the acceleration due to gravity. Include any steps necessary to reduce experimental uncertainty. If needed, you may include a simple diagram of the setup with your procedure.

The students record the time it takes for the ball bearing to fall from different heights. Their collected data is shown below.

Describe how the data collected could be plotted on a graph to determine the acceleration due to gravity.

Figure 1

Figure 1 shows a series of displacement vectors for the motion of a car in one minute intervals.

Derive an expression for the acceleration of the car in terms of , and .

A projectile is fired from level ground with speed  at an angle  to the ground. The projectile is fired from a few centimeters before position , reaches its maximum height at position , and lands on the ground at position .

On the axes provided in Figure 1 sketch a graph of the horizontal and vertical components of the acceleration of the projectile at where . Label the lines and respectively. Add any relevant values to the axes.

Figure 1

A ball of mass is attached to a string and swings in a vertical circle of radius . If the string were cut at the lowest point in its motion, indicate whether a ball would continue to move in a vertical circle, move in a straight line horizontally at the moment of the cut or fall directly to the ground. Justify your reasoning qualitatively.

Figure 1

A group of students conduct an experiment to determine the acceleration of a cart as it moves down a frictionless ramp, as shown in Figure 1. The cart starts from rest at the top of the ramp at . The -axis is defined to be parallel to the ramp, and the position of the cart along the x-axis is recorded at different time intervals.

Table 1 shows the data collected by the students.

Table 1

Indicate two quantities that when graphed yield a straight line whose slope can be used to determine the acceleration of the cart.

Clearly state which variable belongs on the vertical axis and which belongs on the horizontal axis.

Figure 1

A stunt cyclist builds a ramp that will allow the cyclist to coast down the ramp and jump over several parked cars, as shown above. To test the ramp, the cyclist starts from rest at the top of the ramp, then leaves the ramp, jumps over six cars, and lands on a second ramp.

Figure 1 shows the vertical distance between the top of the first ramp and the launch point, , and the angle of the ramp at the launch point, , as measured from the horizontal. The cyclist travels a horizontal distance of whilst the cyclist and bicycle are in the air. The combined mass of the stunt cyclist and bicycle is .

Figure 2

Figure 2 shows the position, , of the stunt cyclist and bicycle as a function of time for the duration of their vertical motion.

On Figure 3, sketch a graph of the vertical component of the stunt cyclist's velocity as a function of time from immediately after the cyclist leaves the ramp to immediately before the cyclist lands on the second ramp. On the vertical axis, clearly label the initial and final vertical velocity components, and . Take the positive direction to be upwards.

Figure 3