Rate of kinetic energy increase equals net force times velocity

Steps:

• Kinetic energy KE = ½ m v²; differentiate to get dKE/dt = m v a = F_net v.
• From force diagram, net force F_net = thrust - drag = 300 kN = 300,000 N.
• Velocity v = 40 m/s.
• Compute power P = F_net × v = 300,000 × 40 = 12,000,000 W = 12 MW.

Why C is correct:

• Matches P = F_net v from work-energy principle, where net force accelerates the aircraft.

Why the others are wrong:

• A. 2.4 MW: Uses a minor force like lift component (60 kN × 40 m/s).
• B. 8.0 MW: Calculates power from drag alone (200 kN × 40 m/s).
• D. 20 MW: Uses gross thrust power (500 kN × 40 m/s), ignoring drag.

Final answer: C