Using the attached Eco$-$Drive game data file, compute the speed profile for the eco$-$drive vehicle assuming that you are only given the acceleration vs time trajectories. Use MATLAB to do the following:

$1.$ Develop a function that relates acceleration to time. Try a polynomial degree of $1,2,3,$ and $4.$ Pick the best choice and explain why it is the best.

$2.$ Create a function file for the equation you developed in a above.

$3.$ Solve the ODE for the equation you developed, with initial speed value of $0.$

$4.$ Show a graph of the modeled speed versus time. Use basic fitting to show the relationship and R$2$ for the speed vs time relationship.