Using the definition of work, we see
and assuming the force is constant, we find, using
that the power can be expressed as
Thus, exerting a force at a larger velocity results in a greater power output, as we intuitively expect.
The units of power can be seen from its definition; they are the units of work (Joules) divided by the units of time (seconds). This combination of units (J/s) is called a Watt (W).
To get an idea of the sizes of the units involved, let us estimate the power output of a person running up a flight of stairs. Assuming the person has a weight of 600 N, and the flight of stairs is 4 m tall, the work done by the person is 600 x 4 = 2400 J. If the person does this in 3 s, the power output is 2400 / 3 = 800 W. One might be familiar with the British unit of power, the horsepower (hp), which was originally defined as the power rate at which an ``typical'' horse could do work, and is still the unit in which the power of car engines is given. The conversion between the two units is that 1 hp = 746 W. The 800 W of power thus exerted by this person is equivalent to 800 W x ( 1 hp / 746 W ) = 1.1 hp.