Power

A particular task may take a certain amount of work to accomplish, but you might take a short time or a long time to carry out the task. The concept of power describes how fast work is being done.

Power is the rate of doing work. It is therefore defined as the time derivative of the work:

\[ \rm \mathbf{P = \frac{dW}{dt}} \]

The average power is the work done divided by the time:

\[ \rm \mathbf{P_{av} = \frac{\Delta W}{\Delta t}} \]

Special case:

If the work is done by a constant force, then we have: P_av = W/t = ( • ) / t = •

The SI-unit of power is the Watt [W]:

1 W = 1 J/s = 1 kg·m²/s³

The dimensionality of power is [P] = [M][L]²/[T]³.

The most common non-SI-unit of power is the horse-power. Conversions:

1 hp = 550 ft lb/s = 745.7 W.

More conversions can be found in the appendix.