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S curve velocity profile
$$area_x = f(velocity,acceleration,jerk)$$
Let's take the easiest, for $area_4$:
$$area_4 = v_{max} * (t_4 - t_3)$$
Where $$v_{max} = {accArea}_1 * (t_3) $$
To calculate this $accArea$ you can utilize … After you find all the formula, and put them to one equation $$distance = f(velocity,acceleration,jerk)$$
You can find each parameter for the distance traveled. …