Solve e=V_{0}t+1/2at^2

$$e = V _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 }$$

Solve for V_0

$$V_{0}=-\frac{at}{2}+\frac{e}{t}$$

$$t\neq 0$$

Steps for Solving Linear Equation

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

$$V_{0}t+\frac{1}{2}at^{2}=e$$

Subtract \frac{1}{2}at^{2} from both sides.

$$V_{0}t=e-\frac{1}{2}at^{2}$$

The equation is in standard form.

$$tV_{0}=-\frac{at^{2}}{2}+e$$

Divide both sides by t.

$$\frac{tV_{0}}{t}=\frac{-\frac{at^{2}}{2}+e}{t}$$

Dividing by t undoes the multiplication by t.

$$V_{0}=\frac{-\frac{at^{2}}{2}+e}{t}$$

Divide e-\frac{at^{2}}{2} by t.

$$V_{0}=-\frac{at}{2}+\frac{e}{t}$$

Solve for a

$$a=-\frac{2\left(V_{0}t-e\right)}{t^{2}}$$

$$t\neq 0$$

Steps for Solving Linear Equation

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

$$V_{0}t+\frac{1}{2}at^{2}=e$$

Subtract V_{0}t from both sides.

$$\frac{1}{2}at^{2}=e-V_{0}t$$

The equation is in standard form.

$$\frac{t^{2}}{2}a=e-V_{0}t$$

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

$$\frac{2\times \frac{t^{2}}{2}a}{t^{2}}=\frac{2\left(e-V_{0}t\right)}{t^{2}}$$

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

$$a=\frac{2\left(e-V_{0}t\right)}{t^{2}}$$