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?

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- Mar 28th 2009, 10:59 AMMissKittyFantasticoFinding Acceleration
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?

- Mar 28th 2009, 11:16 AMchisigma
By definition the mean value of a function $\displaystyle a(t)$ in an interval $\displaystyle t_{1}<t<t_{2}$ is...

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

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Mar 28th 2009, 11:39 AMMissKittyFantastico
So the slope would be the acceleration?

- Mar 28th 2009, 12:14 PMchisigma
In some sense yes... what does matter is that the 'average value' of acceleration in the interval $\displaystyle t_{1}<t<t_{2}$ depends

*only*from the speed at the begginning [$\displaystyle t_{1}$] and the end [$\displaystyle t_{2}$] and not from else...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Mar 28th 2009, 12:40 PMMissKittyFantastico
Okay, thanks.