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What exactly is the difference between $3 \mathrm m/\mathrm s^2$ and $3 \mathrm m/\mathrm s$? According to Wikipedia...

An object experiences a constant acceleration of one metre per second squared (1 m/s²) from a state of rest, when it achieves the speed of 5 m/s after 5 seconds and 10 m/s after 10 seconds.

From this, it seems like that $1 \mathrm m/\mathrm s^2 = 1 \mathrm m/\mathrm s$, though that wouldn't make sense considering how they're treated as separate units.

Port
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  • It's better to think of it as a (meter per second) per second, i.e. (m/s)/s. – icurays1 Apr 10 '14 at 15:09
  • This is a physics question, better ask it there. In short, $m/s$ is a unit of velocity and $m/s^2$ is a unit of acceleration (rate of change of the former). Those are two very different things. – AlexR Apr 10 '14 at 15:40

3 Answers3

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The first one is an acceleration, whereas the second one is a velocity.

For cars it would be "from 0 to 100mph in 3 seconds" (or, strictly speaking, the inverse of that) vs. maximum speed "200mph"...

gerw
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  • Ohh, that already makes much more sense. I was almost interpreting it as a velocity where in a 10 second period, you'd have moved value * sqrt(10) meters or something, and not as an explicit unit for acceleration. Thanks for clearing that up. – Port Apr 10 '14 at 15:16
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The first indicates an acceleration, the second is a velocity.

The acceleration value indicates that with each passing second the associated velocity increases by 3m/s.

While the second value idicates a velocity that does not change with respect to time. As each second passes, the velocity remains at 3m/s.

Chris Cooper
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Consider a snapshot of a space rocket starting with its engines burning, exactly at the moment when it begins to move. Its velocity is still $0 \frac{\mathrm{m}}{\mathrm{s}}$, but its acceleration can be over $20 \frac{\mathrm{m}}{\mathrm{s}^2}$.

Now, imagine a shuttle in space. It might have huge velocity, but without its engines burning (and disregarding the gravity of the Sun, the Earth, the Moon, etc.), its acceleration is zero.

I hope this helps $\ddot\smile$

dtldarek
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