# Power

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## Power

** Question 1:** If two people each carry a weight of 50N up the same hill, which one does more work?

** Question 2:** What if one of them does it in 1 hour and the other takes 2 hours?

The answer to both of the questions above is that they both do the same amount of work. They both carry the same **mass, m** through the same **height, h **so both do

**Work done = mgh**

In the second question, however, the first person completes the work more quickly. They did more work per second. We say that they were more powerful.

**Power is defined as the rate at which you do work.**

**Units:** W, watts. 1 watt = 1 joule per second (= 1 Js^{-1})

*The equation is:*

**Power = Work Done / Time Taken**

Another useful equation can be derived from this. Notice that:

**Work done, W = force x displacement =Fs**

So, power = or

And, = v

So **P =Fv**

So **Power = Force x velocity**; remembering that the force and velocity must be in the **same direction**.