Terminal velocity test with answers for AP Physics C (free PDF download)

Quick answer: Terminal velocity is the steady speed at which a resistive force balances the weight, so the net force is zero. This AP Physics C test on terminal velocity has 8 questions worth 20 marks, to do in 45 minutes: terminal velocity, linear drag calculation and acceleration. The mark scheme is on a separate page; free printable PDF.

This test covers resistive forces, terminal speed, the exponential and tanh solutions, and energy at terminal speed. Use g = 9.81 m/s². Show every substitution and give final numerical answers with units. Calculators are allowed; the time limit is 45 minutes.

Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 2

Time: 45 minutes · 8 questions · Total: 20 marks · Calculator allowed

Contents

Question 1 Terminal velocity (2 marks)

Define terminal velocity. (1 mark)
State the net force on the object at terminal velocity. (1 mark)

Question 2 Linear drag calculation (3 marks)

A ball of mass 0.30 kg falls through oil with F = bv and b = 0.60 kg/s.

Calculate the terminal speed. (1 mark)
Calculate τ. (1 mark)
Calculate the speed 1.0 s after release from rest. (1 mark)

Question 3 Acceleration (2 marks)

For the ball in the previous question:

Differentiate v = v_t(1 − e^−t/τ) to show that a = g e^−t/τ. (1 mark)
State the acceleration at t = 0. (1 mark)

Question 4 Graph (3 marks)

The graph shows the speed of a 0.25 kg bead falling in oil.

Speed of a bead in oil.

State the terminal speed. (1 mark)
Use the drag law F = bv to calculate b. (1 mark)
Estimate τ and check that it agrees with m/b. (1 mark)

Question 5 Parachutist (3 marks)

A parachutist and equipment have mass 65 kg, with F = cv².

With c = 0.22 kg/m before the canopy opens, calculate the terminal speed. (1 mark)
After opening, c = 20 kg/m. Calculate the new terminal speed. (2 marks)