Consider a rabbit that challenges a turtle to a race on a straight line. In this imaginary world, we can assume both the rabbit and turtle accelrate to their respective maximum

speeds instantaneously, meaning we ignore the quadratic term in time for Newton's equation of linear motion. The maximum speed of the rabbit is 8 MPH and the maximum speed of the turle is 2 MPH. The rabbit, being generous, decides to start 6 miles behind the startling line to give a head-start to the turtle. Your objective in this problem is to determine how long it takes the rabbit to catch the turtle and how many miles from the starting line the rabbit passes the turtle. a. b. C. d. e. f. B. h. i. Determine the independent variable and dependent variables of the is problem. What are the units of time and distance for your MATLAB similation? Determine an equation of motion for the rabbit and an equation of motion for the turtle. Load A and b from your equations of motion. A and b define the matrix equation Ax = b. What are the dimensions of matrices A, b, and x? Solve this matrix equation in MATLAB. How long does it take the rabbit to catch the turtle? How many miles from the start line does the rabbit catch the turtle? Plot in MATLAB these two lines and add a symbol of your choosing at the intersection of these two lines indicating your solution (x, y). Hint: use the plot command to plot one point and use the "hold" command. Add an appropriate title and axis labels, it's ok to be creative. Add a grid as well.