Equation 2 shows two other useful equations for power. Power can be expressed as the
rate of change of energy, as you see in the first equation in Equation 2. Sometimes this
is stated as “energy consumption”, as in a 100-watt light bulb “consumes” 100 joules of
energy each second. In other words, the light bulb converts 100 joules of electrical
energy each second into other forms of energy, such as light and heat.
The companies that provide electrical power to homes measure each household’s
energy consumption in kilowatt·hours. You can check that this is a unit of energy. The
companies multiply power (thousands of joules per second, or kilowatts) by time
(hours). The result is that one kilowatt·hour equals 60 kilojoules, a unit of energy.
The second equation in Equation 2 shows that when there is a constant force in the
direction of an object’s displacement, the power can be measured as the product of
the force and the velocity. This equation can be derived from the definition of work:
W = Fǻx. Dividing both sides of that equation by time yields power on the left (work
divided by time). On the right side, dividing displacement by time yields velocity.
As with other rates of change, such as velocity or acceleration, we can consider
average or instantaneous power. Average power is the total amount of work done over
a period of time, divided by that time. Instantaneous power has the same definition, but
the time interval must be a brief instant (more precisely, it is defined as the limit of the
average power as the time interval approaches zero).