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A quantity has dimensions of 𝐿𝑇⁻². What SI unit could this quantity be measured in?

A quantity has dimensions of length times time to the negative two. What SI unit could this quantity be measured in?

In this example, we have some quantity, we’ll call it 𝑄. And the dimensions of 𝑄 are given as length times time to the negative two. Another way to write this is length divided by time squared. We want to know in what SI unit could 𝑄 be measured in. To figure this out, we’ll want to be able to identify the SI unit for length and the SI unit for time.

In the SI system, the base unit in which to express a length is the meter, meanwhile the base unit in which to express a time is the second. So then the SI units of a length divided by a time squared would be meters per second squared. We could also write that using this abbreviation. The SI unit of this quantity then is meters per second squared. These units can give us a sense for what the quantity 𝑄 is. We expect that 𝑄 is an acceleration, since accelerations have these units of meters per second squared.

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