ABSTRACT
When these are implemented on data that contains errors the effect of the error is magnified in the velocity calculation and magnified even further in the acceleration calculation. This is illustrated in Fig. F3.2 for an object that is moving at constant velocity. The left-hand panel shows displacement data and the right-hand panel shows the corresponding velocity as calculated from equation F3.1. When the data has no errors (top row), the result is a velocity value that is constant, reflecting the constant velocity condition that is being analyzed. When the data has one error (middle row – the error introduced by the digitizing process) the effect is to overestimate one of the velocity calculations, but underestimate the next velocity calculation. This gives a spike in the velocity data so, rather than a flat line, the velocity data now gives incorrect values for some of the velocity points. This problem gets worse if the data has two errors in it (bottom row) and it can be seen that the spike in the velocity data becomes worse.
