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The gray is a unit that measures energy absorbed per unit of mass. It's defined as one Joule per one kilogram. Which can be simplified to $m^2/s^2$.

Can you explain the meaning (interpretation) of absorbed dose expressed as square meters per second per second?

I believe this might seem like a silly, very soft question, but in most cases the units do make sense. For example, the fuel consumption is measured in length squared and XKCD manages to provide an explanation of what that area means.

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    $\begingroup$ "Which can be simplified to $m^2/s^2$": you may have reduced the dimensions to base SI units, but you have definetly not simplified in terms of physical interpretation. The original units of $J/kg$ are clearly more intuitive as the amount of energy absorbed per unit mass. $\endgroup$
    – nluigi
    Jun 13, 2019 at 8:16

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Suppose the radiation energy was absorbed as heat by a quantity of ideal gas having mass M (where M is N·m, N is number of molecules, and m is mass of a molecule). Then Q = Δ(KE) = ½ N·m·Δ(v2avg), so Q/M = ½ Δ(v2avg). In that way J/kg corresponds to m2/s2.

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  • $\begingroup$ Or similarly adding 1 joule of kinetic energy into a 1kg block in free space... $\endgroup$
    – Jon Custer
    Jun 13, 2019 at 20:05
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It’s the square of the speed ($m/s$) you’d get if you could convert the radiation energy to kinetic. (Except for an inconvenient factor of two)

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