Power

The power delivered to a system is the rate energy is transfered to it. That means it has the dimensions of energy/time. In SI units this is Joules per second. We call that Watts for short. That should be a familiar unit to you, if you and your friends have ever tried to change a light bulb. If you've ever heard a friend bragging about a car, you might be familiar with the unit of horsepower (hp). $1hp ~=~ 550 ft~lb/s ~=~ 746 W$. So a 25 hp jalopy can keep going a lot of light bulbs!

The average power supplied to say, light bulb, over a time t is

$$\bar P ~=~ {\Delta W\over \Delta t}$$ (1.37)

and the instantaneous power (or power for short) is

$$P ~=~ {dW\over dt}$$ (1.38)

Suppose we have an object and we are pushing it with a force ${\bf F}$, what power do we deliver to the object? Well in a time $t$ we do work ${\bf F}\cdot d {\bf r}$. So the power is

$$P ~=~ {dW\over dt} ~=~ { F\cdot dr\over dt} ~=~ F\cdot v$$ (1.39)