Question

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

Answer 1

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

Explanation:

If you start from this equation

`v_f^2 = v_i^2 - 2 * a * 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 * a * d`

`v_f^2 - v_i^2 = -2 * a * d`

• dividing both sides of the equation by `(-2*d)`

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

This is equivalent to

`a = -(v_f^2-v_i^2)/(2d)`, or

`a = color(green)((v_i^2 - v_f^2)/(2d))`