The questions are on the terminal velocity test. Take it under real conditions before reading the mark scheme.
Quick answer: Terminal velocity is the steady speed at which a resistive force balances the weight, so the net force is zero. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics C test on terminal velocity, from terminal velocity to energy, with the equivalent answers to accept.
Model answers with a marking guide for each question. Award method marks for correct formulae and substitution even if the arithmetic slips, and apply error carried forward where a later part uses an earlier wrong value. Units are required for the final answer.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 2
Question 1 Terminal velocity (2 marks)
a. The constant speed at which the drag force balances the driving force (weight). b. Zero.Marking: 1 mark for each part; part b must say the net force is zero, not the drag.
Question 2 Linear drag calculation (3 marks)
a. vt = mg/b = (0.30 × 9.81)/0.60 = 4.9 m/s. b. τ = m/b = 0.50 s. c. v = 4.905(1 − e−2) = 4.905 × 0.8647 = 4.2 m/s.Marking: 1 mark each; accept 4.9 m/s from 4.905.
Question 3 Acceleration (2 marks)
a. dv/dt = vt(1/τ)e−t/τ = (mg/b)(b/m)e−t/τ = g e−t/τ. b. At t = 0, a = 9.81 m/s².Marking: 1 mark for the derivative with the chain rule, 1 mark for g.
Question 4 Graph (3 marks)
a. 4.0 m/s. b. b = mg/vt = (0.25 × 9.81)/4.0 = 0.61 kg/s. c. The speed is 63 % of 4.0 m/s (2.5 m/s) at 0.40 s, and m/b = 0.25/0.61 = 0.41 s, so τ ≈ 0.40 s agrees.Marking: 1 mark per part; allow ±0.1 s on τ.
Question 5 Parachutist (3 marks)
a. vt = √(mg/c) = √(637.65/0.22) = √2898 = 54 m/s. b. vt = √(637.65/20) = √31.9 = 5.6 m/s.Marking: 1 mark for part a; part b: 1 mark for the substitution, 1 for the result.
Question 6 Heavier object (2 marks)
At terminal speed drag equals weight. A heavier object needs a larger drag force to balance, and drag only grows with speed, so the speed must be larger before the forces balance. Larger weight needs larger speed.Marking: 1 mark for drag = weight; 1 mark for drag increasing with speed.
Question 7 Boat (3 marks)
a. τ = m/b = 250/40 = 6.25 s. b. v = v₀e−t/τ, so t = τ ln(5.0/1.0) = 6.25 × 1.609 = 10 s.Marking: 1 mark for τ; 1 for the rearranged exponential; 1 for the result.
Question 8 Energy (2 marks)
a. P = mg vt = 0.30 × 9.81 × 4.905 = 14 W. b. It comes from the loss of gravitational potential energy, because the kinetic energy is constant.Marking: 1 mark each.
