FRQ : The Remote Controlled Car Race

Assessments aligned to 2026 AP Physics 1 standards

Pause here: To build true exam stamina, attempt these questions on your own before checking the model answers

Scenario: Two remote-controlled cars, Car A and Car B, start from the same position at time t = 0 and race along a straight track. Their velocity-time graphs are shown below.

Car A: Constant velocity of +3.0 m/s for the entire 20.0 s.

Car B: Starts at rest, accelerates uniformly to +6.0 m/s during the first 10.0 s, then remains at +6.0 m/s from t = 10.0 to 20.0 s.

Questions

1️⃣On the same set of axes, sketch the v-t graphs for both Car A and Car B from t = 0 to t = 20 s. Label each car’s graph.

2️⃣Calculate the displacement of each car during the 20.0 s interval. Show the geometric shapes and areas you use for each.

3️⃣At what time, if ever, does Car B overtake Car A? Justify your answer using the areas under the v-t graphs. If Car B never overtakes Car A, explain why not.

4️⃣A student claims that because Car B has a higher final velocity than Car A, Car B must always be ahead after t = 10 s. Design a graphical argument — using position-time graphs or cumulative area analysis — to evaluate whether this claim is correct or incorrect.

Answer Key & Scoring Guide

Sample Response (a):

Car A: Horizontal line at v = +3.0 m/s from t = 0 to 20 s.

Car B: Straight line from v = 0 at t = 0 to v = +6.0 m/s at t = 10 s, then horizontal at +6.0 m/s from 10 to 20 s. The two lines intersect where 3.0 = 0.6t, so at t = 5.0 s.

Car A and Car B (Superimposed graphs)

Scoring (a) — 2 points:

✔️1 pt: Both graphs correctly shaped and labeled

✔️1 pt: Correct numerical values on both axes (v and t values for key points)

Sample Response (b):

Car A: Rectangle area = 3.0 m/s × 20.0 s = 60.0 m.

Car B:

(1) Triangle (0 to 10 s) = ½ × 10.0 s × 6.0 m/s = 30.0 m.

(2) Rectangle (10 to 20 s) = 6.0 m/s × 10.0 s = 60.0 m.

Total for Car B = 30.0 + 60.0 = 90.0 m.

Scoring (b) — 2 points:

✔️1 pt: Correct displacement for Car A (60.0 m) with identified shape

✔️1 pt: Correct displacement for Car B (90.0 m) with identified shapes

 Sample Response (c):

Car B overtakes Car A when their cumulative displacements are equal.

At t = 10 s: Car A has traveled 3.0 × 10 = 30 m. Car B has traveled ½ × 10 × 6 = 30 m. They are at the same position at t = 10.0 s.

After t = 10 s, Car B moves at 6.0 m/s while Car A moves at 3.0 m/s, so Car B pulls ahead.

Therefore Car B overtakes Car A at exactly t = 10.0 s.

Scoring (c) — 3 points:

✔️1 pt: Sets up the equal-displacement condition using areas

✔️1 pt: Correctly calculates that both cars have displacement of 30 m at t = 10 s

✔️1 pt: Correctly concludes Car B overtakes at t = 10 s with justification that Car B’s velocity exceeds Car A’s velocity after this point

 Sample Response (d):

The student's conclusion is correct, but their reasoning is flawed. It is true that Car B is always ahead for t > 10 s, because at exactly t = 10 s, both cars have the same displacement (30 m), and for all times after that, Car B travels at 6.0 m/s while Car A travels at 3.0 m/s.

However, the student's justification—that a higher velocity guarantees being ahead—is incorrect. Position depends on cumulative area under the v-t graph, not just current velocity. For example, from t = 5 s to t = 10 s, Car B has a higher velocity than Car A, but an x-t graph (or cumulative area analysis) shows Car A is still ahead during that entire interval because it built up a larger displacement in the first 5 seconds. Velocity dictates the rate of change of position, not the absolute position itself.

Corrected Scoring (d) — 3 points:

Scoring (d) — 3 points:

✔️1 pt: Correctly evaluates the claim by stating the conclusion (Car B is ahead after 10 s) is true, but the reasoning is invalid.

✔️1 pt: Provides a graphical or area-based argument showing that higher velocity does not mean greater position (e.g., pointing out the interval between 5 s and 10 s where v_B > v_A but x_A > x_B).

✔️1 pt: Clearly articulates that position depends on cumulative displacement (area under the curve) or initial starting conditions, not just instantaneous velocity.

Total: 10 point