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Polinomial model revisited -- a simple calculation of the kinematical parameters of a 100 m sprint
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  • Nataša Janjić,
  • Darko Kapor,
  • Dragan Doder,
  • Jelena Nikolić,
  • Nemanja Gvozdenović
Nataša Janjić
University of Novi Sad Medical Faculty
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Darko Kapor
University of Novi Sad Faculty of Science and Mathematics
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Dragan Doder
Serbian Institute of Sport and Sports Medicine
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Jelena Nikolić
University of Novi Sad Medical Faculty
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Nemanja Gvozdenović
University of Novi Sad Medical Faculty
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Abstract

We summarize and extend here a simple procedure allowing to obtain all important parameters of the 100 m run based on the measured values for the distance S from the start line and expired time t. An example for testing the proposed model are the results for segment values for S and t for elite sprinters, male: C. Lewis, M. Green and U. Bolt, and female: F. Griffith-Jоyner., F. Ashford and H. Drecksler. The distance is approximated by a third order polinomial function S = f(t), which is easily fitted from the split (segment) times. This function is a mathematical model enabling, by using a standard mathematical treatment, to obtain the equations for determining the point of the maximal sprinter velocity vdmax, corresponding to vanishing acceleration, its distance from the start line Sdmax and corresponding time moment tdmax. The function provides direct reading of the initial velocity vo as well as finding the expressions for the sprinter instantaneous velocity vt and acceleration at. It also provides the initial acceleration, enabling to determine the force acting at the begining of the run. Results obtained justified the proposed approach for a universal and practical preparation tool and also showed that there do not exist so large differences in the values of kinematical parameters between analyzed male and female sprinters. The didactical purpose of the paper is to demonstrate how the combination of (unrealistic) exactly solvable model with the knowledge of the realistic behaviour can lead to a good numerical fit.