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

A ball is dropped from rest from a height above the ground. Assume air resistance is negligible.

Derive an expression for the velocity of the ball just before it hits the ground in terms of , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

Air resistance is found to be non-negligible.

On the axis provided in Figure 2, sketch a graph of the velocity of the ball as a function of time from its release to the time just before it hits the ground.

Figure 2

A group of students want to determine the acceleration due to gravity by analyzing the motion of a freely falling object using a ball bearing and an electromagnet. They have access to standard laboratory equipment.

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.

Describe how the data collected in part a) would be graphed, and how that graph would be analyzed 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. The car has velocity at time and displacement at time .

Derive an expression for the acceleration of the car in terms of , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

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

Figure 1

A ball of mass is attached to a rope of length and swings with constant speed in a vertical circle, as shown in Figure 1. At Point A, the ball passes the lowest point in its path, and at Point B, it makes an angle of with the horizontal.

At Point B, the rope is released, and the ball becomes a projectile with the rope still attached.

Indicate whether the range of the projectile with the rope attached is greater than, equal to, or less than the range of the projectile without the rope attached. Justify your reasoning.

Figure 1

An object travels horizontally in a straight line. The graph in Figure 1 shows the velocity of the object as a function of time .

i) On the graph in Figure 1, draw a dotted line to show the average velocity of the object.

ii) Using the graph, determine an expression for the displacement of the object in terms of , and .

Using the graph in Figure 1, determine an expression for the final velocity of the object in terms of , and .

Using the graph in Figure 1, determine an expression for the final position of the object in terms of , , and .

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 -axis is recorded at different time intervals.

Table 1 shows the data collected by the students.

Table 1

Indicate which measured or calculated quantities could be plotted to yield a linear graph whose slope can be used to calculate an experimental value for the acceleration of the cart.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ Vertical Axis ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ Horizontal Axis

Figure 1

Figure 1 shows a simple pendulum which consists of a small sphere that hangs from a string with negligible mass. The top end of the string is fixed. The sphere is pulled to Point X and then released from rest and swings through Point Y to Point Z where it changes direction and swings back.

Sketch a graph of the velocity of the pendulum as a function of position as it undergoes simple harmonic motion.

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