Fitting data to a quadratic function

Question Q6.5.2

The ticker timer, much used in school physics experiments, is a device that marks dots on a strip of paper tape at evenly-spaced intervals of time as the tape moves through it at some (possibly variable) speed. The following data relate to the positions (in cm) of marks on a tape pulled through a ticker timer by a falling weight. The marks are made every 1/10 sec.

x = [1.3, 6.0, 20.2, 43.9, 77.0, 119.6, 171.7, 233.2, 304.2, 384.7,
     474.7, 574.1, 683.0, 801.3, 929.2, 1066.4, 1213.2, 1369.4, 1535.1,
     1710.3, 1894.9]

Fit these data to the function $x = x_0 + v_0t + \frac{1}{2}gt^2$ and determine an approximate value for the acceleration due to gravity, $g$.


Solution

To access solutions, please obtain an access code from Cambridge University Press at the Lecturer Resources page for my book (registration required) and then sign up to scipython.com providing this code.