# Finding Acceleration

• March 28th 2009, 10:59 AM
MissKittyFantastico
Finding 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?
• March 28th 2009, 11:16 AM
chisigma
By definition the mean value of a function $a(t)$ in an interval $t_{1} 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

$\chi$ $\sigma$
• March 28th 2009, 11:39 AM
MissKittyFantastico
So the slope would be the acceleration?
• March 28th 2009, 12:14 PM
chisigma
In some sense yes... what does matter is that the 'average value' of acceleration in the interval $t_{1} depends only from the speed at the begginning [ $t_{1}$] and the end [ $t_{2}$] and not from else...

Kind regards

$\chi$ $\sigma$
• March 28th 2009, 12:40 PM
MissKittyFantastico
Okay, thanks.