The most vivid recollection I have of college calculus is how it reveals the relationships between position, velocity, and acceleration. They, in turn, reveal what motion-control systems need in ...

This is basically just series of lines on the track that the cart uses to determine its position (and thus velocity and acceleration).

In a valid follower motion, the velocity and acceleration will remain continuous throughout the cycle — otherwise the device produces an impossible, infinite amount of jerk.