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The aim of this paper is to bring a mathematical justification to the optimal way of organizing ones effort when running. It is well known from physiologists that all running exercises of duration less than 3mn are run with a strong initial acceleration and a decelerating end; on the contrary, long races are run with a final sprint. This can be explained using a mathematical model describing the evolution of the velocity, the anaerobic energy, and the propulsive force: a system of ordinary differential equations, based on Newtons second law and energy conservation, is coupled to the condition of optimizing the time to run a fixed distance. We show that the monotony of the velocity curve vs time is the opposite of that of the oxygen uptake ($dot{VO2}$) vs time. Since the oxygen uptake is monotone increasing for a short run, we prove that the velocity is exponentially increasing to its maximum and then decreasing. For longer races, the oxygen uptake has an increasing start and a decreasing end and this accounts for the change of velocity profiles. Numerical simulations are compared to timesplits from real races in world championships for 100m, 400m and 800m and the curves match quite well.
Since that very memorable day at the Beijing 2008 Olympics, a big question on every sports commentators mind has been What would the 100 meter dash world record have been, had Usain Bolt not celebrated at the end of his race? Glen Mills, Bolts coach
Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms of engineering on small, intermediate, and large scales.
We use a feed-forward artificial neural network with back-propagation through a single hidden layer to predict Barry Cottonfields likely reply to this authors invitation to the Once Upon a Daydream junior prom at the Conard High School gymnasium back
Blockchain is built on a peer-to-peer network that relies on frequent communications among the distributively located nodes. In particular, the consensus mechanisms (CMs), which play a pivotal role in blockchain, are communication resource-demanding
Astronomy provides a laboratory for extreme physics, a window into environments at extremes of distance, temperature and density that often cant be reproduced in Earth laboratories, or at least not right away. A surprising amount of the science we un