# Power

by Jared Rovny

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00:01 Now we're ready to introduce a new physical quantity.

00:05 We've talked about force and we've talked about distance, but now we're going to ask about power which is how much work am I applying per unit time.

00:13 In other words, how much energy am I giving to a system or taking away from a system per unit time, or how quickly are we doing work. That's measured by power.

00:23 The units of power, since it's equal to a work per unit time, is a force times a distance per unit time which means that the power, since distance over time is velocity, can also be written as the force times the velocity.

00:40 So really there's just two ways you should think about power, one is that it is a force, sorry a work per unit time or you could also think of it as a force times a velocity.

00:50 And the derivation isn't terribly important to memorize but really understand that there are two expressions for power we will be using, one is just the work per unit time and one is a force that's being applied times the velocity of your object.

01:02 The units of power are joules per second because it is work over time.

01:08 So we have energy per unit time, how much energy per time is my system changing or how much energy per time am I giving to my system or taking from my system.

01:17 This unit, joules per second, we call watts and you might be familiar with watts as we'll discuss in a second.

01:23 The important thing is that this unit watts is also represented by a W so we need to be very careful here, because we represented work with the letter W and we're also representing the units of power, which are watts, by the letter W.

01:39 So be very careful here. One of these is a variable, a physical quantity which is work, that's a W as a variable.

01:47 In an equation, you could divide both sides by W or find W in a system.

01:51 Whereas here, the units of power in terms of watts, this W is just a unit, it's not a variable in an equation that you would manipulate or try to find the value of.

02:00 It's just a unit like joules or seconds, and those are watts represented by W.

02:05 And finally, just be very careful with this W, as I've said, because often in equations we see people writing the W as a work unit even though it was really coming from them writing watts somewhere earlier in the problem.

02:21 As a brief overview, now that we've introduced so many variables, we might want to pause and take a look at some of the variables that we've talked about.

02:29 We have now our basic observables the mass of an object, where it is, it's position, velocity, and acceleration, and time through which these things can all change.

02:39 And then we have our basic SI units or international system units.

02:45 In other words, the standard units which we've been using which are kilograms, meters, meters per second, meters per second squared, and seconds for each of the variables on the left respectively.

02:54 Now, in terms of these units, we've introduced force which is in Newtons which we abbreviate as a letter N.

03:02 We have energy which we introduced which can be representing kinetic, potential, or total energy which has units of joules or J.

03:09 We have work which we introduced as also having units of energy because it tells you something about the change in your energy in your system, and now we've introduced power and power has units of W which you can see are the two Ws in very different columns here again representing very different quantities.

The lecture Power by Jared Rovny is from the course Work.

### Included Quiz Questions

1. 5 Watts
2. 5 Joules
3. 5 Newtons
4. 5 Kilowatts
5. 20 Watts
1. mv^2/t
2. ma^2
3. mv^2x
4. mav^2
5. ma^2/t^2
1. 2 Newtons
2. 1 Newton
3. 4 Newtons
4. 5 Newtons
5. 3 Newtons

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