# How would you rework this equation v_f^2= v_i^2 - 2*a*d so that it solves for a?

Jul 20, 2015

You simply isolate $a$ on one side of the equation.

#### Explanation:

If you start from this equation

${v}_{f}^{2} = {v}_{i}^{2} - 2 \cdot a \cdot d$

you can solve for the acceleration of the object, $a$, by

• subtracting ${v}_{i}^{2}$ from both sides of the equation

${v}_{f}^{2} - {v}_{i}^{2} = \cancel{{v}_{i}^{2}} - \cancel{{v}_{i}^{2}} - 2 \cdot a \cdot d$

${v}_{f}^{2} - {v}_{i}^{2} = - 2 \cdot a \cdot d$

• dividing both sides of the equation by $\left(- 2 \cdot d\right)$

$\frac{{v}_{f}^{2} - {v}_{i}^{2}}{\left(- 2 \cdot d\right)} = a \cdot \frac{\cancel{\left(- 2 \cdot d\right)}}{\cancel{\left(- 2 \cdot d\right)}}$

This is equivalent to

$a = - \frac{{v}_{f}^{2} - {v}_{i}^{2}}{2 d}$, or

$a = \textcolor{g r e e n}{\frac{{v}_{i}^{2} - {v}_{f}^{2}}{2 d}}$