Question

If the units of `(A^2/(mass))` are `kgm^2s^-2`, what are the units of `A`?

Answer 1

The unit of `A` is `ms^-1`

Explanation:

This answer may not be the quickest or simplest way to solve this question, but what I'm going to do here is share my own thinking process.

The unit of kinetic energy is the joule (J), but that's not so helpful for this kind of question. Let's try it another way:

`E_k=1/2mv^2`

That is, the kinetic energy is made up of mass measured in `kg` (we can ignore the `1/2`, which is a number without units) and the square of velocity, measured in `ms^-1`, which will be `m^2s^-2`.

That means the units of kinetic energy are `kgm^2s^-2`.

Now, the question says that the units of `(A^2/(mass))` are `kgm^2s^-2`

Canceling out the mass on the left with its units on the right, we get the units of `A^2` as being `m^2s^-2`.

Taking the square root of both sides, the unit of `A` is `ms^-1`.