Solve S=Ut+1/2at^2

$$S = Ut + 1 / 2 at ^ { 2 }$$

Solve for U

$$\left\{\begin{matrix}U=-\frac{at}{2}+\frac{S}{t}\text{, }&t\neq 0\\U\in \mathrm{R}\text{, }&S=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Ut+\frac{1}{2}at^{2}=S$$

Subtract \frac{1}{2}at^{2} from both sides.

$$Ut=S-\frac{1}{2}at^{2}$$

The equation is in standard form.

$$tU=-\frac{at^{2}}{2}+S$$

Divide both sides by t.

$$\frac{tU}{t}=\frac{-\frac{at^{2}}{2}+S}{t}$$

Dividing by t undoes the multiplication by t.

$$U=\frac{-\frac{at^{2}}{2}+S}{t}$$

Divide S-\frac{at^{2}}{2} by t.

$$U=-\frac{at}{2}+\frac{S}{t}$$

Solve for S

$$S=\frac{t\left(at+2U\right)}{2}$$