Solve 1/2at^2=s-ut

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

Solve for a

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

Steps for Solving Linear Equation

The equation is in standard form.

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

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

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

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

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

Solve for s

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