MATLAB QUESTION

Problem 3: A car, initially at rest, accelerates in x direction with the following expression: where a is acceleration and t is time. In this exercise, you are to explore the motion of the car numerically using Euler method. The motion is described by the following differential equations: where u is velocity. Using Euler method and capital letters to denote the approximation, the equations can be approximated by where subscript n denotes variables at current time, subscript n+1 denotes variables at a time that is , ahead. Write function car.m to uerically solve for the motion of the car. The fumction should have the following header: function [T, X, U] car(Tf. dt). The inputs are total traveling time Tf and the time step dt. The outputs vectors T, X and U are the time, distance and velocity of the car, respectively. Give the function a description (a) Set p3azwalc("help car'). (b,c,d) Use function car to get the time, distance, and velocity of the car for T Set the answers to p3b, p3c, and p3d, respectively. Use 10-second time step. 60 s (e,fg) Repeat the step above with 1-second time step. Put the time, distance, and velocity into p3e, pf, and p3g, respectively h) Create figure 1. Use function subplot to include 2 panels with one on top of the other. Plot distance versus time in the top panel. The top panel should include 2 curves: the 10-second time step in parts (b,c) and the 1-second time step in parts (e,f). Plot veloe- ity versus time in the bottom panel. The bottom panel should also inelude 2 curves: the 10-second time step in parts (b,d) and the 1-second time step in parts (eg). Use different solid symbols (no line) for the curves. Set p3h-See figure 1 An 4-point ertra credit wll be given if you include the analytical solution of the distance and velocity in the figure. Use solid line to denote the solution which can be obtained by integrating the differential equations as ou had done in your math/physics class