Skip to main content
We’re so back. See what’s new for the 2026-2027 school year →
The new Teacher Workspace is here. Your first 3 assignments are free. Try it →

AP Physics C: Mechanics Representations FRQ Practice

26 Translation Between Representations questions written in the AP format. Pick one, read the full question, and write your response.

start a random questionbrowse all 26

Your first scored response is included. A plan unlocks unlimited scoring.

New to the Representations FRQ? Read the exam guide

all units
unit 1
unit 2
unit 3
unit 4
unit 6
unit 7

26 questions

sorted by unit

Projectile motion in moving reference frames

Unit 1: Kinematics

Teacher? Assign this question to a class

start this question

A student stands on a platform that moves horizontally at a constant velocity of 3.0 m/s to the right relative to the ground, as shown in Figure 1. At time t = 0, when the student is at position x = 0 relative to the ground, the student throws a ball upward with an initial velocity of 8.0 m/s at an angle of 53° above the horizontal, as measured in the reference frame of the platform. The ball is released from a height of 2.0 m above the ground. Take the +x direction to be to the right and the +y direction to be upward. Air resistance is negligible.

Figure 1: Student on a platform moving right at 3.0 m/s; ball released at height 2.0 m at t = 0 from ground position x = 0

Figure 1

Figure 2: Blank velocity-component axes for drawing the ground-frame initial velocity vector

Figure 2
A.

On Figure 2, draw a vector arrow to represent the initial velocity of the ball as measured in the reference frame of the ground. The tail of the arrow should be placed at the origin. Use an appropriate scale so that the length and direction of the arrow accurately represent the magnitude and direction of the velocity components. The student observes the ball from the reference frame of the ground (Scenario 1).

B.

Derive an expression for the horizontal displacement Δx\Delta x of the ball from its initial position when it reaches maximum height. Express your answer in terms of the platform velocity vp=3.0v_p = 3.0 m/s, the initial speed of the ball relative to the platform v0=8.0v_0 = 8.0 m/s, the angle θ=53°\theta = 53°, the acceleration due to gravity gg, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The ball reaches its maximum height at time t1t_1 as measured from the ground reference frame.

Figure 3: Vertical position y versus time t for the thrown ball (ground frame), from release until it hits the ground

Figure 3

Figure 4: Axes for a_x versus t in the moving-platform frame (Scenario 2), from release until the ball hits the ground

Figure 4
C.

On the axes in Figure 4, sketch a graph of the horizontal component of acceleration axa_x of the ball as a function of time t as measured in the reference frame of the moving platform (Scenario 2). The graph should begin at t = 0 and end when the ball hits the ground. Figure 3 shows the vertical position y of the ball as a function of time t in Scenario 1 (ground reference frame). In Scenario 2, an observer in the reference frame of the moving platform analyzes the horizontal motion of the ball.

D.

Describe one kinematic quantity (position, velocity, or acceleration) that is the same for both balls throughout their motion, and one kinematic quantity that is different for the two balls throughout their motion. For each quantity you identify, briefly justify your answer with reference to the motion of the balls. In Scenario 3, a second identical ball is dropped from rest at the same instant and from the same height (2.0 m) as the thrown ball. Both balls are observed from the ground reference frame.

What the Representations FRQ asks

The Translation Between Representations (TBR) question is FRQ 2 on the AP Physics C: Mechanics exam. You represent one mechanics scenario as a diagram, a derived equation, and a sketched graph, then describe and justify a feature of the motion.

25–30 min
suggested on the exam
12 points
across parts A to D
95 min
for all four FRQs
read the exam guide

  1. Part A: Diagram

    Draw a bar chart, vector arrows, or a force diagram

    3 pts

  2. Part B: Derivation

    Derive an expression for a key quantity, starting from a fundamental principle

    4 pts

  3. Part C: Graph

    Sketch a graph of a related quantity, such as angular velocity versus time

    3 pts

  4. Part D: Reasoning

    Describe a feature of the scenario, or how it would change, and justify it

    2 pts

How Representations FRQ practice works

Each question follows the exam’s format, from the full prompt to a score on every part.

  1. Read the full question

    The scenario, its figures, and parts A through D, laid out the way the exam shows them.

  2. Write on a 27-minute timer

    Inside the 25 to 30 minutes the exam suggests for this question. Pause it or turn it off, and your response saves as you go.

  3. Submit for a score out of 12

    Your response is scored against the scoring guidelines written for that question. Your first score is included.

Feedback on every part

A summary at the top tells you what to work on next. Below it, each part shows whether you earned the point and what the scoring guidelines were looking for.

start a random question

Detailed Feedback

Part A: 1/1 point

Earned the point. You correctly drew and labeled the gravitational force pointing downward and the tension force pointing upward on the block.

Part A: 0/1 point

Did not earn the point. Your free-body diagram for the disk is missing the upward normal/axle force from the mount. The disk should have three forces: gravity (down), tension (down), and the axle force (up).

Part A: 1/1 point

Earned the point. You correctly drew the gravitational force vector longer than the tension vector on the block, indicating it accelerates downward, and you did not include any extraneous forces.

Detailed feedback on a practice Representations FRQ

Questions about the Representations FRQ

How many responses can I get scored?

You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring.

What representations does the TBR ask for?

A diagram such as an energy bar chart, velocity vectors, or a force diagram, then a derivation, a graph of a related quantity, and a written description of a feature of the scenario.

How is the TBR different from the Mathematical Routines question?

Both include derivations. The TBR is built around linking a diagram, an equation, and a graph of the same scenario, and it is worth 12 points instead of 10.

How do I draw the bar chart or graph?

Use the drawing tool to draw on the question’s figure or on a blank graph. Your drawing is scored with the rest of your response. You can also switch to handwrite and add a photo of your page.

Are these real College Board questions?

No. We wrote them in the AP format, with the same four parts, and wrote scoring guidelines for each one.

More AP Physics C: Mechanics practice

Mathematical Routines FRQ practice

Mathematical Routines questions with the full scenario, figures, and both parts.

start practicing

Experimental Design FRQ practice

Experimental Design questions with the lab setup, the data table, and all four parts.

start practicing

Qualitative/Quantitative FRQ practice

Qualitative/Quantitative Translation questions with the full scenario and all three parts.

start practicing

AP Physics C: Mechanics FRQs

Every FRQ type for AP Physics C: Mechanics, with practice for each.

see every question type

AP Physics C: Mechanics study guides

Unit-by-unit review for the whole course.

read the guides

Write your first Representations FRQ

Pick one from the list, or let us choose for you.

start a random questionchoose a unit

Teaching AP Physics C: Mechanics? Assign these Representations FRQs to your class