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# Interpreting units in formulas

Video transcript

- [Voiceover] Consider
the formula P is equal to W divided by T where P represents power, W represents work and has units of Joules and Joules can be expressed as kilograms times meters squared
per seconds squared and T represents time and
has units of seconds. And when you get to physics
class you'll get very familiar with things like Joules
which can be represented as kilograms times meters squared per seconds squared and things like power. But here we're going
to learn to manipulate these units so that they make sense. So it says select an appropriate
measurement unit for power. And 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. So the units for work...the units for work right over here is Joules. And 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 meters squared per seconds squared so lets do that. So this is going to be equal to Joules we can re-write as kilogram times meters squared over seconds squared and we are going to divide all of that by seconds. And so what's that going to be? Well we could re-write this,
this is going to be kilograms (and I'm intentionally trying
not to skip any steps), kilograms times meters
squared per seconds squared and dividing by seconds
is the same thing as multiplying by 1 over seconds. So times 1 over seconds and
so 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 meters squared or kilogram times square meters over the denominator
you have seconds squared times seconds, you have
seconds to the third power. So a unit for power, one way
to express the units for power, could be kilogram meters
squared per second cubed. And we see that this is this first choice kilograms meters squared
per seconds cubed.