Model for assessment of the velocity and force at the start of sprint race

A mathematical model was developed for the assessment of the starting velocity and initial velocity and force of a 100-m sprint, based on a non-homogeneous differential equation with the air resistance proportional to the velocity, and the initial conditions for t = 0, v = v(0). The use of this model requires the measurement of reaction time and segmental velocities over the course of the race. The model was validated by comparison with the data obtained from 100-m sprints of men: Carl Lewis (1988), Maurice Green (2001) and Usain Bolt (2009), and women: Florence Griffith-Joyner, Evelyn Ashford and Drechsler Heike (1988) showing a high level of agreement. Combined with the previous work of the authors, the present model allows for the assessment of important physical abilities, such as the exertion of a high starting force, development of high starting velocity and, later on, maximisation of the peak running velocity. These data could be of importance for practitioners to identify possible weaknesses and refine training methods for sprinters and other athletes whose performance depend on rapid movement initiations.