Parametric polygon synthesizer

This is one of a set of applets designed to be a problem posing playground for teachers. The left hand panel shows the trajectory in space traced out by a moving object. The right hand panel shows the horizontal and vertical motions of that object as functions of time. The user can control - - the number of intervals during which the object moves with constant speed (links) - the times at which the speed of the object may change (black dots) - the horizontal position of the object at those instants of time (lower right hand panel) - the vertical position of the object at those instants of time (upper right hand panel) What problems could/would you set for your students based on this applet?