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I need to be able to define a specific amount of time that a move will last, and calculate what the peak velocity should be when all other factors are known. Starting velocity is not always zero, but ending velocity will always zero for my purposes. The move will always be trapezoidal.

I have an equation for defining the distance traveled when all other factors are known, but I need to isolate the peak velocity to one side of the equation and I am not sharp enough at this math to be able to solve for the peak velocity. Any help would be greatly appreciated.

Assuming:

d = total distance traveled

t = total time

AC = acceleration

DC = deceleration

Vi = initial velocity

Vs = slewing (peak) velocity

Vf = final velocity

I have this equation which I believe is correct. I need to isolate Vs to one side:

d = [(Vs+Vi)/2]*[(Vs-Vi)/AC] + [(Vs+Vf)/2]*[(Vf-Fs)/DC] + Vs*[t-((Vf-Vs)/DC)-((Vs-Vi)/AC)]

I was advised to put it in quadratic form and isolate the Vs but I have found that very difficult. Please help me solve this!

Thanks