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The actual expression for accelleration is metres per second per second. Because speed is metres per second, and the concept of accelleration is how fast is speed changing... in other words if something is travelling at 10 metres per second at Time A, and it is travelling at 20 metres per second at Time B, we know that it increased by 10 metres per second, but if we know the difference between Time A and Time B we can then say how fast that change was occurring.

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Acceleration is the rate of change of velocity. In other words, it is velocity divided by time. So its SI unit of measurement should be spoken as, 'metre per second per second', not 'metre per second squared'.

Strictly speaking, therefore, its symbol should be m/s/s which, of course, is the same as m/s2 (where the 2 is a superscript).

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Q: Why is acceleration defined as meters per second squared?
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