Cue Column:

• Definition?
• Instantaneous vs average?
• Units?

Notes:

Average Power: P_avg = W/t = total work / total time

Instantaneous Power: P = dW/dt = F . v = Fv*cos(theta)

SI Unit: Watt (W) = J/s = kg*m^2/s^3 Dimension: [ML^2T^{-3}] 1 Horsepower (HP) = 746 W

Constant Power Problems: If engine delivers constant power P to a vehicle of mass m: P = Fv = mav (if no friction) mv*(dv/dt) = P Integrating: (1/2)mv^2 = Pt v = sqrt(2Pt/m) — velocity proportional to sqrt(t)

Terminal/Maximum Velocity: When friction = driving force: P = f_friction * v_max v_max = P/f_friction

Summary: Power is how fast work is done. Constant power does NOT mean constant force or constant acceleration.