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

1 Answer
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*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)#