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Math Help - Finding Acceleration

  1. #1
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    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?
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  2. #2
    MHF Contributor chisigma's Avatar
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    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
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  3. #3
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    So the slope would be the acceleration?
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  4. #4
    MHF Contributor chisigma's Avatar
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    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
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  5. #5
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    Okay, thanks.
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