Hey guys,
Can anyone help me solve the following equation for t?
Thanks!
Jordan
$s = u t + \dfrac 1 2 a t^2$
$\dfrac 1 2 a t^2 + u t - s = 0$
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}$