Equation rearranging s=ut+1/2at^2?

Question

Hi, could someone walk me through rearranging the equation s=ut+1/2at^2 for a and for t. I'm pretty sure i've been able to rearrange it for a; a = sqrt (s/t), but the t variable i'm struggling with owing due to the fact that the equation has 2 t's in it. Any help would be appreciated, thanks.

Answer 1

s = ut + (1/2) a t^2

therefore

(1/2) a t^2 = s - ut

(1/2) a = (s - ut)/t^2
a = 2(s - ut)/t^2


And to get t it's a little harder and you have to use quadratics.

s = ut + (1/2)a t^2

So

(1/2)a t^2 + ut - s = 0

Which is a quadratic of the form
ax^2 + bx + c = 0

To solve for t, the zero's occur at

t = (-u +/- SQRT(u^2 + 2.a.s)) / a

Answer 2

i get a=(2s-2ut)/t^2 and 1/t-at=u-2s