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I'm just a little bit confused about the $m/s^2$ in acceleration.

If an object is accelerating at $10m/s^2$, does it mean that every second, it speeds up at $10m/s$?

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    $\begingroup$ yes, you are right $\endgroup$ Aug 18, 2017 at 8:03

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If an object is accelerating at $10m/s^2$, does it mean that every second, it speeds up at $10m/s$?

Yes, exactly. It is the change of velocity over time, so for example how much change in velocity (m/s) you have per second. So the unit of acceleration is meters per second per second, or just per square second.

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Your assumption was correct, as long as the acceleration is constant (which I think is enough for this question's purpose). Acceleration is defined as the change of velocity over a given period of time. In other words, the ratio between the change in velocity and the period of time: $$a=\frac{\Delta v}{\Delta t}$$ You know the units for velocity and time: $$[\Delta v]_{SI}=\frac{m}{s},\:\:\:[\Delta t]_{SI}=s$$ Replacing in the original formula: $$[a]_{SI}=\frac{[\Delta v]_{SI}}{[\Delta t]_{SI}}=\frac{\frac{m}{s}}{s}=\frac{m}{s^2}$$

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Yes, you are right if the object is accelerating at constant acceleration. You can see this best from the definition for the acceleration:

$$a=\frac{\Delta v}{\Delta t},$$ so in $\Delta t = 1~\mathrm{s}$ the velocity changes by $\Delta v=10~\mathrm{m/s}$ (if $a=10~\mathrm{m/s}^2$), or in $0.1~\mathrm{s}$ the velocity changes by $1~m/s$.

If your acceleration is not constant you would replace the differences by derivatives:

$$a=\frac{dv}{dt},$$

but the meaning stays essentially the same, only that you have infinitesimals now. An acceleration of $10~\mathrm{m/s}^2$ you could then (in a non-mathematical physicist kind of way) depict as a change of velocity by $0.00000000001~\mathrm{m/s}$ in $0.000000000001~\mathrm{s}$ (or some other small numbers)

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Yes you are correct, Acceleration is the rate of change of velocity, in short if you are accelerating the more the time passes the more is your velocity and the distance travelled. The m/s2 of acceleration is actually meter per second per second (m/s / s) which is the rate of change of velocity so summing up the indices it is written as m/s^2.

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