This material can be used by an instructor to enrich a lecture or can be assigned to students for individual perusal.
It is useful at two levels. First, it may be used to enhance students' understanding of functions. The height of the bouncing ball, plotted against time, is a series of parabolas. This gives a nice and natural example of a function that analytically must be defined piece-wise. Similarly the velocity gives an example of a naturally discontinuous function.
Second, it can serve to enrich students' understanding of the relation between acceleration, velocity and displacement. The example is considerably more interesting than the usual "falling body;" determining the height function algebraically (a suggested homework assignment) is a realistic and challenging exercise.