Solve for a v^2=v_0^2+2ax

$v^{2} = {v_{0}}^{2} + 2 a x$

Step 1

Rewrite the equation as ${v_{0}}^{2} + 2 a x = v^{2}$ .

${v_{0}}^{2} + 2 a x = v^{2}$

Step 2

Subtract ${v_{0}}^{2}$ from both sides of the equation.

$2 a x = v^{2} - {v_{0}}^{2}$

Step 3

Divide each term in $2 a x = v^{2} - {v_{0}}^{2}$ by $2 x$ and simplify.

Divide each term in $2 a x = v^{2} - {v_{0}}^{2}$ by $2 x$ .

$\frac{2 a x}{2 x} = \frac{v^{2}}{2 x} + \frac{- {v_{0}}^{2}}{2 x}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a x}{2 x} = \frac{v^{2}}{2 x} + \frac{- {v_{0}}^{2}}{2 x}$

Rewrite the expression.

$\frac{a x}{x} = \frac{v^{2}}{2 x} + \frac{- {v_{0}}^{2}}{2 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{a x}{x} = \frac{v^{2}}{2 x} + \frac{- {v_{0}}^{2}}{2 x}$

Divide $a$ by $1$ .

$a = \frac{v^{2}}{2 x} + \frac{- {v_{0}}^{2}}{2 x}$

Simplify the right side.

Move the negative in front of the fraction.

$a = \frac{v^{2}}{2 x} - \frac{{v_{0}}^{2}}{2 x}$