Solve 5=ut+1/2at^2

$$5 = u t + \frac { 1 } { 2 } a t ^ { 2 }$$

Solve for a

$$a=-\frac{2\left(tu-5\right)}{t^{2}}$$

$$t\neq 0$$

Steps for Solving Linear Equation

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

$$ut+\frac{1}{2}at^{2}=5$$

Subtract ut from both sides.

$$\frac{1}{2}at^{2}=5-ut$$

The equation is in standard form.

$$\frac{t^{2}}{2}a=5-tu$$

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

$$\frac{2\times \frac{t^{2}}{2}a}{t^{2}}=\frac{2\left(5-tu\right)}{t^{2}}$$

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

$$a=\frac{2\left(5-tu\right)}{t^{2}}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{\sqrt{u^{2}+10a}+u}{a}\text{; }t=-\frac{-\sqrt{u^{2}+10a}+u}{a}\text{, }&a\neq 0\text{ and }a\geq -\frac{u^{2}}{10}\\t=\frac{5}{u}\text{, }&a=0\text{ and }u\neq 0\end{matrix}\right.$$