Finding Acceleration

**MissKittyFantastico** · Mar 28th 2009, 10:59 AM

How do you find the average acceleration of an object over a certain amount of time if you are given the start and end time and the different velocities at each time?

**chisigma** · Mar 28th 2009, 11:16 AM

By definition the mean value of a function $a(t)$ in an interval $t_{1}<t<t_{2}$ is...

$m[a(t)] =\frac {\int_{t_{1}}^{t_{2}} a(t)\cdot dt}{t_{2}-t_{1}}$

But the primitive of acceleration $a(t)$ is $v(t)$ so that...

$m[a(t)]= \frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}$

Kind regards

$\chi$ $\sigma$

**MissKittyFantastico** · Mar 28th 2009, 11:39 AM

So the slope would be the acceleration?

**chisigma** · Mar 28th 2009, 12:14 PM

In some sense yes... what does matter is that the 'average value' of acceleration in the interval $t_{1}<t<t_{2}$ depends only from the speed at the begginning [ $t_{1}$ ] and the end [ $t_{2}$ ] and not from else...

Kind regards

$\chi$ $\sigma$

**MissKittyFantastico** · Mar 28th 2009, 12:40 PM

Okay, thanks.

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