I\'ve had several people ask me about the one kinematic equation we didn\'t real

Question

I've had several people ask me about the one kinematic equation we didn't really interpret all that explicitly: vf2=vi2+2ax. I sort of had to dodge the question...it wasn't quite clear what a squared velocity meant. I could say that either a bigger acceleration (bigger "a") and/or a longer distance spent accelerating (bigger "x") would lead to a bigger change in velocity, but that was about it. Now we can interpret that squared velocity equation a little better. It's really just our work-energy equation in disguise. Your job here is to do a little quick algebra to turn vf2=vi2+2ax into Wnet=KEf-KEi. Outline your algebra steps and then say a few words on interpreting vf2=vi2+2ax in light of the work-energy equation. (Hint: first notice "a" can be written as F/m).

Explanation / Answer

see Wf=Wi + F.x so 1/2 *m*vf^2=1/2*m*vi^2+ m*a*x so dividing by m/2 vf^2=vi^2+2ax

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