Mechanical systems, an engine for example, are not limited by the amount of work
they can do, but rather by the rate at which they can perform the work. This
quantity, the rate at which work is done, is defined as power.
Equations for Power
From this very simple definition, we can come up with a simple equation for the
average power of a system. If the system does an amount of work, W, over a
period of time, T, then the average power is simply given by:
= 

It is important to remember that this equation gives the
average power
over a given time, not the instantaneous power. Remember, because in the equation
w increases with
x, even if a constant force is exerted, the
work done by the force increases with displacement, meaning the power is not
constant. To find the instantaneous power, we must use calculus:
P = 

In the sense of this second equation for power, power is the rate of change of
the work done by the system.
From this equation, we can derive another equation for
instantaneous power that does not rely on calculus. Given a force that acts at
an angle θ to the displacement of the particle,
Since
= v
,
Though the calculus is not necessarily important to remember, the final equation
is quite valuable. We now have two simple, numerical equations for both the
average and instantaneous power of a system. Note, in analyzing this equation,
we can see that if the force is parallel to the velocity of the particle, then
the power delivered is simply
P = Fv.
Units of Power
The unit of power is the joule per second, which is more commonly called a
watt. Another unit commonly used to measure power, especially in everyday
situations, is the horsepower, which is equivalent to about 746 Watts. The rate
at which our automobiles do work is measured in horsepower.
Power, unlike work or energy, is not really a "building block" for further
studies in physics. We do not derive other concepts from our understanding of
power. It is far more applicable for practical use with machinery that delivers
force. That said, power remains an important and useful concept in classical
mechanics, and often comes up in physics courses.