# For the equation v_f^2=v_i^2 + 2ad, how do you solve for v_i?

Jun 29, 2015

#### Answer:

You isolate ${v}_{i}^{2}$ on one side and take the square root from both sides of the equation.

#### Explanation:

The equation

${v}_{f}^{2} = {v}_{i}^{2} + 2 \cdot a \cdot d$, where

${v}_{f}$ - the final speed;
${v}_{i}$ - the initial speed;
$a$ - the acceleration of an object;
$d$ - its displacement.

establishes a relationship between an accelerating object's initial and final speeds and the total displacement.

So, to solve for ${v}_{i}$, simply isolate ${v}_{i}^{2}$ on one side of the equation

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

then take the square root from both sides of the equation

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

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