An object starts out at t=0, s=0 and accelerates with A=sin(pi*t/T), where T is defined as (pi/2 * Vmax/Amax). Vmax is maximum velocity, and Amax is maximum acceleration. Solution is restricted to t=0 to t=T
The velocity equation is v(t) = 0.5Vmax(1-cos(pi*t/T))
What I am trying to solve is velocity as a function of displacement, v(s).
In other words, without having access to elapsed time, I am trying to generate an equation for velocity as a function of the observed displacement.
Is this possible?