Cue Column:

• Definition?
• Instantaneous vs average?
• Units?

Notes:

Average Power: $P_{avg}$ = $\frac{W}{t}$ = total work / total time

Instantaneous Power: P = $\frac{dW}{dt}$ = F . v = Fv*cos(theta)

SI Unit: Watt (W) = $\frac{J}{s}$ = 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*$\frac{dv}{dt}$ = P Integrating: \frac{1}{2}$$mv^2 = Pt v = sqrt$\frac{2Pt}{m}$ — velocity proportional to sqrt(t)

Terminal/Maximum Velocity: When friction = driving force: P = $f_{friction}$ * $v_{max}$ $v_{max}$ = $\frac{P}{f_friction}$

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