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Math Help - Basic integration kinematics question

  1. #1
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    Basic integration kinematics question

    Can someone please show me how to do this question?
    I know you have to antidifferentiate twice to get the displacement function but am i not sure exactly what to integrate.

    A body moves in a straight line with an acceleration of 10 m/s^2
    If after 2 seconds it passes through O and after 3 seconds is 25 metres from O, find its initial displacement relative to O.

    Do I start off with a=10t ?

    Thanks, help is appreciated
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  2. #2
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    Quote Originally Posted by user_5 View Post
    Can someone please show me how to do this question?
    I know you have to antidifferentiate twice to get the displacement function but am i not sure exactly what to integrate.

    A body moves in a straight line with an acceleration of 10 m/s^2
    If after 2 seconds it passes through O and after 3 seconds is 25 metres from O, find its initial displacement relative to O.

    Do I start off with a=10t ?

    Thanks, help is appreciated
    a = 10 \Rightarrow \frac{dv}{dt} = 10 \Rightarrow v = 10t + C.

    v = 10t + C \Rightarrow \frac{dx}{dt} = 10 t + C \Rightarrow x = 5 t^2 + Ct + K .

    Substitute x(2) = 0: 0 = 20 + 2C + K .... (1)

    Substitute x(3) = 25: 25 = 45 + 3C + K .... (2)

    Solve equations (1) and (2) simultaneously for C and K. Substitute the values for C and K into x = 5 t^2 + Ct + K .

    To get initial displacement, substitute t = 0.
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