Solve Deltas=1/2*a*Deltat^2

$$\Delta s = \frac { 1 } { 2 } \cdot a \cdot \Delta t ^ { 2 }$$

Solve for a

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

$$\frac{\Delta t^{2}}{2}a=s\Delta$$

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

$$\frac{2\times \frac{\Delta t^{2}}{2}a}{\Delta t^{2}}=\frac{2s\Delta }{\Delta t^{2}}$$

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

$$a=\frac{2s\Delta }{\Delta t^{2}}$$

Divide \Delta s by \frac{1}{2}\Delta t^{2}.

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

Solve for s

$$\left\{\begin{matrix}\\s=\frac{at^{2}}{2}\text{, }&\text{unconditionally}\\s\in \mathrm{R}\text{, }&\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\Delta s=\frac{a\Delta t^{2}}{2}$$

Divide both sides by \Delta .

$$\frac{\Delta s}{\Delta }=\frac{a\Delta t^{2}}{2\Delta }$$

Dividing by \Delta undoes the multiplication by \Delta .

$$s=\frac{a\Delta t^{2}}{2\Delta }$$

Divide \frac{a\Delta t^{2}}{2} by \Delta .

$$s=\frac{at^{2}}{2}$$