1. The problem statement, all variables and given/known data My question uses the following problem. I am confused as to why s=v(bar) * t works out the same as s=(v0-vfinal)/2 * t Enlighten me please! Problem: How long does it take to fall 1000ft with no drag? What is the final velocity? displacement: s=1000ft acceleration: a=9.8 (gravity) time: t=? 2. Relevant equations s=v(bar) * t (distance = average rate * time) s=(1/2)at2 (distance = one half * acceleration * time squared) v=at 3. The attempt at a solution Step 1) Convert 1000ft to 304.8 m Step 2) Rearrange s=(1/2)at2 to t=sqrt[2a/d] Step 3) Plugin known variables and solve for t giving 7.887 s Step 4) Plugin known variables into v=at giving v=77.29 m/s Step 5) Check answer with s=v(bar) * t 304.8 m = (384.8-0)/(7.887-0) * 7.887 s I see that step 5 also works if you use this equation s = [(v0-vfinal)/2] * t Why is this the case?