Evaluate a formula for data in a file
We consider the formula y(t) = v0t - 0.5gt2 and want to evaluate y for a range of t values found in a file with format
v0: 3.00
t:
0.15592 0.28075 0.36807889 0.35 0.57681501876
0.21342619 0.0519085 0.042 0.27 0.50620017 0.528
0.2094294 0.1117 0.53012 0.3729850 0.39325246
0.21385894 0.3464815 0.57982969 0.10262264
0.29584013 0.17383923
More precisely, the first two lines are always present, while the next lines contain an arbitrary number of t values on each line, separated by one or more spaces.
a) Write a function that reads the input file and returns v0 and a list with the t values.
b) Write a function that creates a file with two nicely formatted columns containing the t values to the left and the corresponding y values to the right. Let the t values appear in increasing order (note that the input file does not necessarily have the t values sorted).
c) Make a test function that generates an input file, calls the function for reading the file, and checks that the returned data objects are correct. Filename: ball_file_read_write.py