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Thread: Solve for t

  1. #1
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    Solve for t

    Hey guys,

    Can anyone help me solve the following equation for t?

    Thanks!

    Jordan
    Attached Thumbnails Attached Thumbnails Solve for t-img_5185.jpg  
    Last edited by Jordan1010; Sep 29th 2017 at 12:31 AM.
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  2. #2
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    Re: Solve for t

    $s = u t + \dfrac 1 2 a t^2$

    $\dfrac 1 2 a t^2 + u t - s = 0$

    assuming $a\neq 0$

    $t^2 + \dfrac {2u}{a}t - \dfrac{2s}{a} = 0$

    complete the square

    $\left(t + \dfrac u a\right)^2 - \dfrac{u^2}{a^2}-\dfrac{2s}{a} = 0$

    $\left(t + \dfrac u a\right)^2 = \dfrac{u^2 +2as}{a^2}$

    $\left(t + \dfrac u a\right) = \pm \sqrt{\dfrac{u^2 +2as}{a^2}} = \pm \dfrac{\sqrt{u^2 +2as}}{a}$

    $ t = -\dfrac u a \pm \dfrac{\sqrt{u^2 +2as}}{a} = \dfrac{-u \pm \sqrt{u^2+2as}}{a}$
    Thanks from HallsofIvy and topsquark
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  3. #3
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    Re: Solve for t

    Hey Romsek,

    Thanks for the reply! that has helped heaps!

    Cheers again,

    Jordan
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