Consider again the distance/time plots of the two sprinters shown in Fig. 13.5 at the beginning of Section 13.2. If we let x denote distance (in m), and t denote time (in s) then each sprinter’s path can be described by the general function x = vmt − vm(1 − e −βt )/β, for some constants vm and β. For Usain Bolt vm = 12.333 m/s and β = 0.68851/s while for Florence Griffith-Joyner vm 11.008 m/s and β = 0.68947/s.

For each sprinter calculate their velocity and acceleration as a function of time. What is their maximal velocity? Show that the maximal acceleration of each sprinter is vm β.