Power

How fast, not how much. The AP Physics 1 CED defines power as the rate at which energy changes with respect to time, either by transfer into or out of a system or by conversion from one type to another within a system.

The equation sheet prints two forms.

• Average power, $P_{\text{avg}} = W/\Delta t = \Delta E/\Delta t$, the energy transferred or converted divided by the time the transfer took.
• Instantaneous power, $P_{\text{inst}} = F_{\parallel} v = F v \cos\theta$, for the component of a constant force parallel to the object's velocity.

The unit is the watt, one joule per second. Power is a scalar, and it can be negative when energy is leaving the system.

The distinction that costs marks is power against work. A 100 W motor and a 1000 W motor can raise the same crate to the same shelf and do identical work; the second one is finished in a tenth of the time. Any question phrased around how long or how quickly is a power question even when the word never appears.

The second form is why a car has a top speed. The engine delivers a roughly fixed power, and $P = Fv$ means the driving force available shrinks as speed rises, until it can no longer exceed the drag pushing back.

AP Physics C: Mechanics writes the instantaneous form as a derivative, $P_{\text{inst}} = dW/dt$.