On the performance of Usain Bolt in the 100 m sprint

Many university texts on mechanics consider the effect of air drag force, using the slowing down of a parachute as an example. Very few discuss what happens when the drag force is proportional to both u and u(2). In this paper we deal with a real problem to illustrate the effect of both terms on the speed of a runner: a theoretical model of the world-record 100 m sprint of Usain Bolt during the 2009 World Championships in Berlin is developed, assuming a drag force proportional to u and to u(2). The resulting equation of motion is solved and fitted to the experimental data obtained from the International Association of Athletics Federations, which recorded Bolt's position with a laser velocity guard device. It is worth noting that our model works only for short sprints.