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

Answer:

In a nutshell, units of A and B are $\frac{1}{[l]^{2}}$ and $\frac{[l]}{[t]}$, respectively.

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:

$A = \frac{[l]}{[l]^{3}}$

$A = \frac{1}{[l]^{2}}$

$B = \frac{[l]}{[t]}$

In a nutshell, units of A and B are $\frac{1}{[l]^{2}}$ and $\frac{[l]}{[t]}$, respectively.