Using matlab, write code to solve the following problem:

The (x,y) coordinates of a certain object as a function of time t are given by x(t) = 5t -10 and y(t) =25t^2 - 120t + 144 for 0 less than or t less than or 4. Write a MATLAB program to determine the time at which the object is the closest to the origin at (0,0). Determine also the minimum distance. Do this in two ways: [3-a]. By using a for loop (i.e., using scalar code) [3-b]. By not using a for loop (i.e., using vectorization code)