The time rate of doing work. The symbol often used for power is P . If work is denoted by W , then
\begin
[P \equiv \frac
]\end
Since work is force exerted over displacement, the work done by a constant force over a displacement is given by
\begin
[ W = \vec
\cdot \vec
]\end
If the force is constant, then its derivative with respect to time is zero. and we have
\begin
[ P = \frac
= \vec
\cdot \frac{d
}
= \vec
\cdot \vec
]\end
The unit of power is the Watt (symbol W ), which is equal to 1 Joule/second . In CGS units, power is expressed in ergs/second (of which there are 107 per Watt), but which has no other name. In "English" units power is expressed as horsepower (abbreviated hp), where 1 hp = 745.7 W
James Watt himself came up with the expression "horsepower" and the first definition in order to compare the power of steam engines to that of horses doing the same work, and he did the first estimate of the mechanical work horses were capable of. Note that our conversion factor is the current commonly accepted one for strictly mechanical work. There are other definitions of "horsepower" for other applications that are not quite the same.