Power equals resistive force times velocity, with force proportional to speed squared

Steps:

• Resistive force F ∝ v²; at v = 20 m/s, F = 800 N.
• At v = 40 m/s, F = 800 × (40/20)² = 800 × 4 = 3200 N.
• Power P = F × v = 3200 × 40 = 128000 W = 128 kW.

Why C is correct:

• P = Fv gives exactly 128 kW, as force quadruples and velocity doubles at twice the speed.

Why the others are wrong:

• A: Underestimates by using original force with doubled speed (800 × 40 / 1000 = 32 kW).
• B: Assumes linear force scaling, yielding half the required power.
• D: Overestimates by cubing the speed ratio incorrectly (8 × 64 kW).

Final answer: C