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Why only this S. I unit is taken like $m/s^2$ of acceleration?
Because acceleration$=\frac{change\ in\ velocity}{time}$
We know $meter/second$ or $m/s$ is the SI unit of velocity and $second$ or $s$ is the SI unit of time.
Therefore, SI unit of acceleration $=\frac{m/s}{s}=m/s^2$
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