Question

A particle moves along a path described by y=Ax^3 ​​ and x = Bt, where tt is time. What are the units of A and B?

Answer 1

In a nutshell, units of A and B are
`(1)/([l]^(2))` and
`([l])/([t])`, respectively.

Step-by-step explanation:

From Dimensional Analysis we understand that
`x` and
`y` have length units (
`[l]`) and
`t` have time units (
`[t]`). Then, we get that:

`[l] = A\cdot [l]^(3)` (Eq. 1)

`[l] = B\cdot [t]` (Eq. 2)

Now we finally clear each constant:

`A = ([l])/([l]^(3))`

`A = (1)/([l]^(2))`

`B = ([l])/([t])`

In a nutshell, units of A and B are
`(1)/([l]^(2))` and
`([l])/([t])`, respectively.