Answer to Question #97691 in Algebra for belle

Question

Make the subject of the formula S=ut+1/2 at2

Answer 1

$S=ut+\frac{1}{2}at^2\\u=\frac{1}{t}(S-\frac{1}{2}at^2)\\a=\frac{2(S-ut)}{t^2}\\t=\frac{-u+\sqrt{u^2+2aS}}{a}\;or\;t=\frac{-u-\sqrt{u^2+2aS}}{a}$

Since $t\ge0$, if a>0, only the first solution is valid, if a<0 both solutions are valid.