# What does $\mathrm{ms}^{-1}$ mean?

A baseball is hit with a velocity of $28.0 \ \mathrm{ms}^{-1}$. Should I just ignore this, or is it actually part of the question, what does it mean?

• $1 m \; s^{-1} = 1\; m/s$ is one meter per second. That's the same thing as 3.6 km/h and again the same thing as roughly 2.24 mph – t.b. Aug 28 '11 at 13:03
• Shouldn't this be migrated to the physics SE? – J. M. is a poor mathematician Aug 28 '11 at 16:28
• – Willie Wong Aug 29 '11 at 13:00

It means meters per second (recall that $s^{-1}=1/s$, so $m \;s^{-1}=m/s$).

• And, strictly speaking, units should be in roman type 28.0 $\mathrm{m s}^{-1}$ not italic 28.0 $m s^{-1}$ – GEdgar Aug 28 '11 at 13:27
• I would also suggest a space between the units, as in $28.0\;\mathrm{m\;s}^{-1}$, lest it be misinterpreted as "$28.0$ per millisecond". – Ilmari Karonen Aug 28 '11 at 17:41
• Or even $28.0\ \text{m} \cdot \text{s}^{-1}$. – Tanner Swett Aug 28 '11 at 22:06

It's never wise to ignore an element of a question. In the case of physical quantities the dimensions are required. Consider the alternative: a baseball is hit with a velocity of 28. 28 what? meter per hour? inch per second?

More interestingly, suppose that you had computed this answer, and it turned out that the resulting velocity is 28 meter per second per second (m/s^2). This is not the correct dimension for a velocity (it is for acceleration) and so it would alert you of an error in the computation.

This is an example of Dimensional Analysis.

• "a velocity of 28.28 what?" In doubt, megaparsecs per Planck time... – leftaroundabout Aug 28 '11 at 23:50