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

1 hour29 questions
1a
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2 marks

State the conditions required for kinematic equations to be used.

1b
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2 marks

A position-versus-time graph has a slope of 1.

What can be inferred from this information about the motion of the object? Justify your answer.

1c
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2 marks

The slope of a velocity-versus-time graph is negative 1.

What can be inferred from this information about the motion of the object? Justify your answer.

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2a
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2 marks

The slope of an acceleration-versus-time graph is 2.

What can be inferred from this information about the motion of the object? Justify your answer.

2b
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2 marks

Describe the procedure to determine the change in velocity of an object using an acceleration-versus-time graph.

2c
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2 marks

Describe the procedure to determine the acceleration of an object using a velocity-versus-time graph.

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3a
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2 marks
Graph showing velocity versus time, with a curve rising from point A, passing through B and C, and flattening at D, indicating decreasing acceleration.

Figure 1

Figure 1 shows the velocity of a skydiver. Identify the section of the graph that represents the skydiver reaching terminal velocity. Justify your answer.

3b
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2 marks

Describe the motion of the skydiver between points A and C in Figure 1.

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4a
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1 mark

A teacher tells her physics students that 'motion is relative'. Explain what the teacher means by this.

4b
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3 marks

After class, some students are discussing the lesson. Student A makes the following claim:

"The magnitude of the displacement of an object is not relative."

Identify whether Student A is correct or incorrect.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ correct ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ incorrect

Justify your reasoning.

4c
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1 mark

Student B argues that Student A's claim is only valid for an inertial reference frame.

Explain what is meant by inertial reference frame.

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5
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1 mark

A police car is driving on a long straight stretch of the freeway. At t space equals space 0, the police car's position is 200 space straight m north of a farmhouse. 400 space straight m north of the farmhouse, a car has broken down on the side of the road.

Determine the position of the police car at t space equals space 0 from the reference frame of the broken down car.

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1a2 marks

A ball is dropped from rest from a height of 2.0 space straight m above the ground.

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

1b
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3 marks

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.

Graph showing velocity (m/s) against time (s). Horizontal line marks terminal velocity. Note: "Time when ball hits the ground" at graph end.

Figure 2

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2a
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4 marks

A group of students want to determine the acceleration due to gravity g 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.

2b
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4 marks

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

Drop height/m

Fall time/s

0.50

0.32

0.75

0.39

1.00

0.45

1.25

0.50

1.50

0.55

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

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3
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2 marks
Horizontal line with multiple arrows pointing right, labeled with vectors Δx₁ to Δx₉, representing a sequence of movements or changes.

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 increment x, v subscript x space 0 end subscript and t. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

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4
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2 marks

A projectile is fired from level ground with speed v subscript 0 at an angle theta to the ground. The projectile is fired from a few centimeters before position x subscript 1, reaches its maximum height at position x subscript 2, and lands on the ground at position x subscript 3. end subscript.

On the axes provided in Figure 1 sketch a graph of the horizontal and vertical components of the acceleration of the projectile at t space equals space 0 where y space equals space 0. Label the lines a subscript x and a subscript y respectively. Add any relevant values to the axes.

Graph with x-axis labelled "t" and y-axis labelled "a". The axes intersect at the origin, with grid lines in the background.

Figure 1

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1
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3 marks
Diagram of a circular path for an object moving counterclockwise. Point A is marked at the bottom of the circle and Point B is marked at 30 degrees above the horizontal.

Figure 1

A ball of mass m is attached to a rope of length L and swings with constant speed v 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 30 degree 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.

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2a
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3 marks
Graph showing a line with constant positive slope, representing velocity (v in m/s) versus time (t in s), indicating constant acceleration. The graph starts from a velocity which is not equal to zero.

Figure 1

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

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 v subscript x, v subscript x space 0 end subscript and t.

2b
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2 marks

Using the graph in Figure 1, determine an expression for the final velocity of the object in terms of v subscript x space 0 end subscript, a subscript x and t.

2c
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3 marks

Using the graph in Figure 1, determine an expression for the final position of the object in terms of x subscript 0, v subscript x space 0 end subscript, a subscript x and t.

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3
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2 marks
Diagram of a cart at the top left of a sloped ramp, labelled "Cart," with an arrow showing positive x direction and the point x = 0 marked.

Figure 1

A group of students conduct an experiment to determine the acceleration a 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 t space equals space 0. The x-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.

Position x (m)

Time t (s)

0.06

0.39

0.14

0.59

0.24

0.77

0.37

0.96

0.55

1.20

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 a of the cart.

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

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4
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2 marks
Diagram of a pendulum with three positions: X (left, solid line), Y (centre, dashed line), and Z (right, dashed line) from a fixed point.

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.

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5
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2 marks
Stunt motorcyclist jumps over five cars, launching from a ramp with initial height \(H_0\) and angle \(\theta_0\), covering horizontal distance \(X_0\).

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, H subscript 0, and the angle of the ramp at the launch point, theta subscript 0, as measured from the horizontal. The cyclist travels a horizontal distance of X subscript 0 whilst the cyclist and bicycle are in the air. The combined mass of the stunt cyclist and bicycle is m subscript 0.

Graph with a grid background showing a curve on an xy-plane, labelled 'y' and 't'. The curve starts high, dips low, peaks, then slightly declines.

Figure 2

Figure 2 shows the position, y, 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, v subscript y space 0 end subscript and v subscript y. Take the positive direction to be upwards.

Graph with x-axis labelled "Time" and y-axis labelled "Vertical Component of Stunt Cyclist's Velocity," featuring a grid on a grey background.

Figure 3

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