Interpreting units in formulas | Mathematics I | High School Math | Khan Academy

Consider the formula P is equal to W / T where P represents power, W represents the work and has units of joules. Joules can be expressed as kilogram times meter squared per second squared, and T represents time and has units of seconds.

When you get to physics class, you'll get very familiar with things like joules, which can be represented as kilogram times meters per second squared, and things like power. But here we're going to learn to manipulate these units so that they make sense.

So it says to select an appropriate measurement unit for power. What we've seen multiple times in our mathematical careers is that, on a certain level, you can manipulate units in a lot of the same ways that you would manipulate variables or numbers.

So, if power is equal to work divided by time, we could also say that the units for power are going to be the units for work divided by the units for time.

The units for work right over here is joules. So we could write it's going to be joules per... and then the unit for time is seconds. So you might want to say it's joules per second. But we don't see joules per second as a choice here, so we probably want to expand out joules as being kilogram meter squared per second squared.

So let's do that. This is going to be equal to joules. We can rewrite joules as kilogram times meter squared over second squared, and we're going to divide all of that by seconds.

And so what's that going to be? Well, we could rewrite this. This is going to be kilograms... and I'm intentionally trying not to skip any steps. Kilograms times meter squared per second squared, and dividing by seconds is the same thing as multiplying by 1/seconds, so times 1 over seconds.

If we treat these units the way that we might treat things like variables, this would be equal to, in the numerator, we would have kilogram times meter squared or kilogram times square meters.

In the denominator, you have seconds. You have seconds to the third power. So a unit for power, one way to express the units for power, could be kilogram meter squared per second cubed. And we see that this is this first choice: kilogram meter squared per second cubed.