1. ## Solve for t

Hey guys,

Can anyone help me solve the following equation for t?

Thanks!

Jordan

2. ## 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

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

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

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

$t = -\dfrac u a \pm \dfrac{\sqrt{u^2 +2as}}{a} = \dfrac{-u \pm \sqrt{u^2+2as}}{a}$

3. ## Re: Solve for t

Hey Romsek,

Thanks for the reply! that has helped heaps!

Cheers again,

Jordan