Modelling Sprint Mechanics: A Comparative Analysis of Work Done by an Elite and Amateur Athlete using Differential Equations

This investigation compares the velocity, acceleration, and work done by an elite sprinter and an amateur during a 100m race. The author utilizes 10m split data to develop displacement-time models, transitioning from quartic regression to a more biomechanically accurate first-order differential equation (da/dt = -ka) to model acceleration as exponential decay.

By integrating acceleration and velocity functions, the author calculates total work done using the integral of force over time. Findings reveal a significant disparity in work output (approximately 6003 J vs 2574 J). The paper is distinguished by its critical refinement of mathematical models and a thorough evaluation of air resistance and human reaction time.