Question

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

Answer 1

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*a*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 * a * d`

then take the square root from both sides of the equation

`sqrt(v_i^2) = sqrt(v_f^2 - 2 * a * d)`

`v_i = sqrt(v_f^2 - 2 * a * d)`