Rate of increase of kinetic energy is net power input, m v a

Steps:

• Kinetic energy KE = ½ m v²; differentiate with respect to time: dKE/dt = m v (dv/dt) = m v a.
• Identify given values: m = 3000 kg, v = 15 m/s, a = 0.5 m/s² (net acceleration determines rate regardless of resistive force breakdown).
• Compute m a = 3000 × 0.5 = 1500 N (net force).
• Compute dKE/dt = 1500 × 15 = 22500 W.

Why B is correct:

• Applies the formula dKE/dt = m v a from the chain rule of differentiation for kinetic energy.

Why the others are wrong:

• A likely misapplies ½ m a v or ignores velocity factor.
• C may stem from approximate arithmetic error in m v a.
• D could result from using resistive force alone without net acceleration.

Final answer: B