Solve for m e=1/2*(mv^2)

$e = \frac{1}{2} \cdot (m v^{2})$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (m v^{2}) = e$ .

$\frac{1}{2} \cdot (m v^{2}) = e$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (m v^{2})) = 2 e$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (m v^{2}))$ .

Multiply $\frac{1}{2} (m v^{2})$ .

Combine $m$ and $\frac{1}{2}$ .

$2 (\frac{m}{2} v^{2}) = 2 e$

Combine $\frac{m}{2}$ and $v^{2}$ .

$2 \frac{m v^{2}}{2} = 2 e$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{m v^{2}}{2} = 2 e$

Rewrite the expression.

$m v^{2} = 2 e$

Step 4

Divide each term in $m v^{2} = 2 e$ by $v^{2}$ and simplify.

Divide each term in $m v^{2} = 2 e$ by $v^{2}$ .

$\frac{m v^{2}}{v^{2}} = \frac{2 e}{v^{2}}$

Simplify the left side.

Cancel the common factor of $v^{2}$ .

Cancel the common factor.

$\frac{m v^{2}}{v^{2}} = \frac{2 e}{v^{2}}$

Divide $m$ by $1$ .

$m = \frac{2 e}{v^{2}}$