Solve S=wt+1/2at^2

$$S = w t + \frac { 1 } { 2 } a t ^ { 2 }$$

Solve for a

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

Steps for Solving Linear Equation

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

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

Subtract wt from both sides.

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

The equation is in standard form.

$$\frac{t^{2}}{2}a=S-tw$$

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

$$\frac{2\times \frac{t^{2}}{2}a}{t^{2}}=\frac{2\left(S-tw\right)}{t^{2}}$$

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

$$a=\frac{2\left(S-tw\right)}{t^{2}}$$

Solve for S

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