Construct the time-displacement graph for a flat-surface tracker moving through a maximum displacement of 34 inches.

It consists of a complete upward harmonic movement from 0 to 55, followed by a rest that is half the maximum displacement, up to 101, later , it has a complete upward cycloidal movement up to 193.The descent consists of three parts, a constant acceleration up to 237, a constant speed up to 299 and finally a deceleration for the rest of the trajectory. Using the displacement equations, determine:

a) Minimum length for the follower face (f(x)). As an answer, give the value of this length with a positive sign