# Power

The amount of work done by a body or on a body is related to the change in the body's motion (more precisely to its kinetic energy). The notion of work is important in understanding how much we could potentially change a body's motion. However, it makes a big difference whether the work done on an object was over a year vs. if we the work done on an object was in 6 seconds, even if the amount of work involved in both cases is the same.

What distinguishes these two situations is the amount of work that was done in a given amount of time. This is known as power, the rate of change of work with time:

$$ P = \frac{dW}{dt} $$

In the case where the power delivered over some time \( T \) is a constant, \( P_c \), we get:

$$ P_c T = W \rightarrow P_c = \frac{W}{T} $$

The difference between a lot of power and little power, given the same amount of work done, is the time.

The standard dimension by which power is measured is the watt, which is:

$$ 1 watt = joule / s $$