EXPERIMENT 3. FREE FALL ANALYSIS so that an object moving in 1-dimension with constant acceleration has a displacement of the form y ( t ) = y0 + v0 t + 1 2 at 2 Since we have an expectation for the functional form of the measurements of the displacement versus time, we can use a process called curve ﬁtting to determine the parameters of the function relating the measured quantities. In this case the initial position y0 , initial velocity v0 and the acceleration a are the parameters relating displacement to time. Knowing these parameters would allow one to calculate the displacement y calc ( t ) at any time and plot a continuous curve. Because of uncertainty in measurements, however, the measured data points would not be expected to lie exactly on this curve (although the range they include -denoted by “error bars” should overlap the plot for 68% of the data). When given a set of data points one can seek the parameters of the function that provide the best matching of the calculated values to the measured values. Starting with some
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