Power = rate of doing work. P = dW/dt = F.v (instantaneous). Average power = total work / total time.

Constant power motion: P = mav = constant. As v increases, a decreases. v = sqrt(2Pt/m). The vehicle never has constant acceleration under constant power.

Terminal/maximum velocity: When driving force = friction: v_max = P/f. On an incline: v_max = P/(f + mg*sin(theta)).

Practical applications: Pumps (P = mgh/t), elevators (P = Mgv), engines. Always account for efficiency: P_useful = eta * P_input.

Key insight: Power determines how FAST work can be done, not how much. A small engine can do the same total work as a large one, just takes longer.