Solve V=ut+1/2ad^2

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

Solve for a

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

Steps for Solving Linear Equation

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

$$ut+\frac{1}{2}ad^{2}=V$$

Subtract ut from both sides.

$$\frac{1}{2}ad^{2}=V-ut$$

The equation is in standard form.

$$\frac{d^{2}}{2}a=V-tu$$

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

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

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

$$a=\frac{2\left(V-tu\right)}{d^{2}}$$

Solve for V

$$V=\frac{ad^{2}}{2}+tu$$