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Teachers & SchoolsStudy Guide

Finally, with our knowledge of momentum and energy, we've reached the end goal of every physics student, aspiring politician, and James Bond villain: unlimited power. And while Auric Goldfinger might have had to achieve this via some exceedingly complicated plot involving nerve gas, gold paint, and a squat manservant with a penchant for nice hats, our route to power is much more straightforward.

**Power** (*P*) is the rate at which an object can do work (*W*). In contrast to Goldfinger's plans, the power expended by an object in interval Δ*t* is given by a very simple formula.

No need to run from the nerve gas, either. Because work is the product of force and distance, we can express the power expended by object A equivalently in terms of the force (*F*) object A is exerting on object B and the speed (*v>/em>) object B is moving at.*

*P* = *Fv*

Remember, *v* would be given by the distance object B traveled divided by the time it took to travel that distance, Δ*t*, so this works out. Just like work, however, this formula only applies if *F* is applied in the same direction as motion.

The SI unit of power is J/s, which is called a watt (W). Be careful not to confuse power and energy—power is an instantaneous rate of energy transfer. You might have some 60 W light bulbs in your house, meaning they radiate 60 J of energy per second as light and heat when you turn them on. But your electricity provider will charge you by the kilowatt-hour (kWh)*, a unit of energy representing the total of all the light bulbs in your house multiplied by all the seconds they've been on.

*1 kWh = 3.6 × 10^{6} J, so it tends to remove a lot of zeros from their spreadsheets.

The formula *P* = *Fv* is straightforward, but you have to remember that the object expending the power to make the force doesn't have to be the object moving at speed *v*. Two examples: in a car, the engine combusts gasoline to generate power that makes a force to move the car forward; the more horsepower*, the faster the car can move. But a hang glider uses force from the wind to move (so *F* would come from the wind) and *v* from the glider, together giving us the power the wind uses to move the glider.

*1 hp = 746 W

Perhaps the most famous use of a watt in history (past, present, and future) comes from *Back to the Future*, when Marty McFly tries to convince the past version of Doc Brown to generate 1.21 GW by hitting his DeLorean with lightning—which is a huge amount of power.