Footrace: the concept of derivative

The proposed activity on the concept of derivative is based on the visualisation of the speed of change of kinematic quantities. There are three graphs made with GeoGebra representing the timing laws of three athletes competing in a footrace. Athletes tackle the race with different strategies which correspond to the hourly charts represented by y=x^2,y=x and y=√x. The activity is to explore the performance of the graphs, whose generating functions are kept hidden, to answer a series of questions concerning the comparative speed of the athletes, the meaning of derivative as the slope of the tangent and how its variation is related to the concavity of the hourly chart. The activity ended with a discussion of the initial moments of the race and on the recognition of functions that represent the three hourly equations.


Antonio Criscuolo

Material Type
derivative  kinematic 
Target Group (Age)
English (United Kingdom)
GeoGebra version
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