Question

Which of the following are dimensionally equivalent?
I. vaxt^2
II. xv
III. 2a/v^2
IV. x^2/t^2
V. x^3/2t

Answer 1

Hi! When you look at these, you want to look at what type of quantities are involved (like distance, time, distance per time, etc.).

So do that for each.
\(v\) is distance per time
\(x\) is distance
\(t\) is time

Answer 2

and \(a\) is distance per time per time.

All those come from knowing what the variables commonly mean.

So, for example, I is
\(v\ a\ x\ t^2\)
distance per time \(\times\) distance per time per time \(\times\) distance \(\times\) time times time
\[\frac{distance}{time}\times\frac{distance}{time\ \ time}\times distance\times time\ \ time\]

\[\frac{distance}{time}\times\frac{distance}{\cancel{time}\ \ \cancel{time}}\times distance\times \cancel{time}\ \ \cancel{time}\]

\[\rightarrow \frac{distance\ \ distance\ \ distance}{time}\]

Any questions? It gets easier as you understand what you're doing!