Solve for x v^2=v_0^2+2a(x-x_0)

$v^{2} = {v_{0}}^{2} + 2 a (x - x_{0})$

Step 1

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

${v_{0}}^{2} + 2 a (x - x_{0}) = v^{2}$

Step 2

Simplify each term.

Apply the distributive property.

${v_{0}}^{2} + 2 a x + 2 a (- x_{0}) = v^{2}$

Rewrite using the commutative property of multiplication.

${v_{0}}^{2} + 2 a x + 2 \cdot - 1 a x_{0} = v^{2}$

Multiply $2$ by $- 1$ .

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

Step 3

Move all terms not containing $x$ to the right side of the equation.

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

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

Add $2 a x_{0}$ to both sides of the equation.

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

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ .

Cancel the common factor.

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

Divide $x_{0}$ by $1$ .

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

Solve for x v^2=v_0^2+2a(x-x_0)

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