Solve s=ut+1/2at^2u

$$s = u t + \frac { 1 } { 2 } a t ^ { 2 } u$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{2\left(tu-s\right)}{ut^{2}}\text{, }&u\neq 0\text{ and }t\neq 0\\a\in \mathrm{R}\text{, }&\left(t=0\text{ or }u=0\right)\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ut+\frac{1}{2}at^{2}u=s$$

Subtract ut from both sides.

$$\frac{1}{2}at^{2}u=s-ut$$

The equation is in standard form.

$$\frac{ut^{2}}{2}a=s-tu$$

Divide both sides by \frac{1}{2}t^{2}u.

$$\frac{2\times \frac{ut^{2}}{2}a}{ut^{2}}=\frac{2\left(s-tu\right)}{ut^{2}}$$

Dividing by \frac{1}{2}t^{2}u undoes the multiplication by \frac{1}{2}t^{2}u.

$$a=\frac{2\left(s-tu\right)}{ut^{2}}$$

Solve for s

$$s=\frac{tu\left(at+2\right)}{2}$$