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Square seconds, by itself, doesn't make much sense. On the other hand, please note that acceleration is not the same as speed or velocity, therefore you would expect the units to be different between the two. Speed or velocity is measured in meters / second; since acceleration is the change of rate of a velocity (in symbols: dv/dt), its units are velocity / time. Using SI units, that would be (meters / second) / second, and this is commonly written as meters / second2, which makes sense since the seconds appear twice in the denominator.

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