1. The problem statement, all variables and given/known data I dont know if the title is misleading or not because I cant think of anything better .. I need help with something Ive been working on... its not homework...its more of a side project/hobby of mine, but i couldnt figure out where to put this question.. Basically I need to figure out the x-component of the initial velocity So lets call it Vi Heres the scenario http://img27.imageshack.us/img27/5536/sce1d.jpg [Broken] The known values are d1= 10 d2= 10 d3= 10 a = 10 during d1 and d3 and a = 0 during d2 (see pic above) and t1+ t2 + t3 = 3 seconds 2. Relevant equations Vf = Vi + a*t d= Vit + 0.5*a*t^2 d = v*t (if acceleration = 0) vf^2 = vi^2 + 2ad So basically I started off with the following 3 equations, I only used the first three equations from above d1 = Vi*t1 + 0.5*a*t1^2 d2 = V2*t2 (since acceleration = 0) Since V2 = Vi + at1, then d2 = (Vi + a*t1)t2 = Vi*t2 + a*t1*t2 d3 = V2*t3 + 0.5*a*t3^2 or in terms of Vi d3 = Vi*t3+ a*t1*t3 + 0.5*a*t3^2 3. The attempt at a solution d1+d2+d3= Vi*t1 + 0.5*a*t1^2 + Vi*t2 + a*t1*t2 + Vi*t3+ a*t1*t3 + 0.5*a*t3^2 Then I rearranged the equation to get dtotal = Vi(t1+t2+t3) + (0.5*a*t1^2 + a*t1*t2 + at*t1*t3 + 0.5*a*t3^2) Mutiply both sides by 2 to get rid of 0.5 2*dtotal = 2*Vi(t1+t2+t3) + a(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2) After plugging in the known values, this is the point Im stuck at 60 = 6*Vi + 10(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2) Is there any way I can reduce the above equation knowing t1+t2+t3 = 3 to find out Vi? Or maybe Im doing this completely wrong and theres a better way to find out Vi given the scenario??