Section 5.2 Power
The rate of doing work is called power.
\begin{equation*}
\therefore P=\frac{\,dW}{\,dt} = \frac{\vec{F}\cdot\,d\vec{x}}{\,dt}
\end{equation*}
\begin{equation*}
=\vec{F}\cdot\frac{\,d\vec{x}}{\,dt} =\vec{F}\cdot\vec{v}
\end{equation*}
\begin{equation*}
\left[\text{also,}\quad w=\int P\,dt\right]
\end{equation*}
Power defines how fast has the work been done. It’s unit is Watt = W = Joule/s (in SI unit), erg/s = erg per sec (in cgs unit), and ft-lb/s = foot-pound per second (in fps unit).
The old and more common unit of power is horse power (hp) 1hp = 746 W = 550 ft-lb/s.