I think it's
Dimensional formulas use mass, length, and time to express physical quantities as a propduct of powers of fundamental quantities.
Since velocity is defined as distance divided by time, you can say that
This means that the dimensional formula for velocity will have
This tells you that
- you have no units of mass in equation, since
#"M"#is raised to the power of zero;
- you have units of length, meters, raised to the power of 1;
- you have units of time, seconds, raised to the power of negative 1;
So, take the equation for escape velocity and test to see if these are the units that you're left with for the dimensional formula.
If you use units, the equation will look like this
As far as units are concerned, this will give you
As you can see, this confirms the initial dimensional formula, since you have meters multiplied by seconds to the power of negative 1. Therefore, the dimensional formula for escape velocity is