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

1 Answer
Jul 20, 2015

Answer:

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))#