 So let's take a look at a couple more derived units. The basic unit of time is the second. And this gives us some additional derived units. And to find these, we can go to our definitions. For example, speed is the distance an object travels divided by how long it takes the object to travel the distance. So what are the units of speed? So we have speed is equal to distance divided by time. And if we measure distance in meters and time in seconds, we get units of meters divided by seconds. Now it's important to recognize that that works if we measure distance in meters and time in seconds, but we could measure speed using other units. So again, speed is distance divided by time. And if we measure our distance in kilometers and time in hours, we get kilometers per hour as a unit of speed. And we can even use bizarre units to get things like speed as, so I don't know, maybe we'll measure distance in feet and time in fortnights. So feet per fortnight is also a unit of speed. One more important derived unit is density. And density is the amount of mass divided by the amount of, well, space. So mass is usually measured in grams, g, or kilograms, kg, and space is measured in, well, different things. For example, if a 50 meter wire has a mass of three kilograms, let's find the density and the units. So the density, usually abbreviated with the Greek letter rho, because density begins with an r, is the mass divided by the space. So here the units are helpful to tell us what these numbers are, even if we weren't told that three kilograms was the mass, the fact that it's measured in kilograms tells us that three kilograms is a mass, so we know the mass. And the amount of space, the only thing here that takes up space is the length of the wire, 50 meters. So again, units act just like algebraic variables, so we have three kilograms divided by 50 meters, and so that's 350 kilograms divided by meters, and we can compute the numerical value, 0.06, and our units, kilograms per meter. Now, because this is mass per unit of length, we sometimes call this a linear density. Now, an important idea once we hit higher mathematics is the idea of a change, and an important idea is that the change of a quantity is measured in the same units as the quantity. So if a person's height changes from 1.5 meters to 1.8 meters, they grew by 0.3, that's the numerical value, and the units are the same meters. Similarly, if an object's mass changes from 250 kilograms down to 80 kilograms, the numerical difference is 170, and the units are still kilograms. And so this brings up another important idea. If an object's speed changes, it undergoes an acceleration, and the amount of acceleration is the change in speed divided by how long the change took. Now, strictly speaking, acceleration does involve a little bit more than that, but as far as the units are concerned, this is what's important. And if we measure speed in, well, how about meters per second, the change in speed is also measured in meters per second, and so we get change in speed, meters per second, divided by time, we'll use seconds again. To simplify this, we might begin by noting that meters per second is really the same as meters divided by seconds, and we can simplify by multiplying numerator and denominator by seconds. And that gives us meters per second squared as a unit of acceleration.