Analysing Usain Bolt using GeoGebra/Document: Difference between revisions

The red graphs are the velocity and acceleration models from Bejing 2008, with Berlin 2009 in blue and London 2012 in green. The first thing we notice is that there is a remarkable similarity between the shapes of the graphs and the closeness of fit of the displacement-time graph to the data. In each case the acceleration graphs have a minimum, a maximum and a zero which effectively divide each run into 4 stages. After an initial acceleration off the blocks of around 10 ms^-2, the first stage of around 4 seconds corresponds to a decrease in the acceleration to around zero. Then there is a second stage up to just over 6 seconds when he accelerates again to around 1 ms^-2at around 57m. After this there is a third stage until around 7.5 seconds when his acceleration becomes zero and he hits his maximum velocity of around 13 ms^-1at around 75m. The fourth and final stage is until he crosses the finishing line. It is here that there is most difference between the runs – depending on closely challenged Bolt was at that stage. In Bejing he had left the field standing, and started his celebrations well before crossing the line! This accounts for the low value of his final velocity and the extent of his deceleration, as well as a less good fit for the displacement data at the end of the race. What we can now do is to try to predict the time Bolt might have recorded had the race been more closely fought so that he had keep running at his best right until the finishing tape. We just need to experiment with the value in cell B12. So it must just have been that he had the potential to record a world record shattering 9.5 seconds if only the other runners had kept pace!