Qualitative/quantitative translation (QQT)

Car accelerating with constant engine power

Units 1, 2 and 3
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 15–20 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.

The question

A car of mass m starts from rest on a straight, level road at time t = 0. Its engine delivers a constant power P to the car, and all of that power goes into the car's kinetic energy (ignore friction losses and air resistance). A student claims: “Because the engine's power stays constant, the car's acceleration also stays constant.”

Suggested time: 18 minutes

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Part (a)

3 points

Do you agree or disagree with the student's claim? Justify your answer without using equations.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the car's speed v(t) and acceleration a(t) as functions of time, in terms of P, m, and t.

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

Explain how your expressions from part (b) support your answer to part (a). Then use them to predict how the time to go from speed $v_1$ to $2v_1$ compares with the time to go from rest to $v_1$ .

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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