Anaconda Jupyter Notebook Assignment

In a Jupyter notebook, use the following Python code to generate ‘experimental’ data for distance travelled (x_exp) under constant acceleration for various times t, given a model (x_model).

a, v_o, x_o = (1.0, 0.05, 2.54)
t = linspace(0, 5, 100)
x_model = 0.5*a*t**2 + v_o*t + x_o
noise = 0.25*randn(100)
x_exp = x_model + noise
  • How many data points are there? (answer in a markup cell) (1 pt)
  • What is the standard deviation you should use in your chi-square calculation? (answer in a markup cell) (1 pt)

Next, in Python calculate chi-square using the ‘experimental’ and model values above.

  • How many degrees of freedom do you expect for this problem? Is chi-square close to the number of degrees of freedom? (answer in a markup cell) (2 pts)

Lastly, calculate chi-square for the same data, but for a different model where v_o = 0.

  • What does your value of chi-square tell you about your fit? (answer in a markup cell) (1 pt)  
  • Plot your data and the two models, with a legend and axis labels. (5 pts)

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