required to stop an automobile is a function of velocity (v). The following experimental data was collected to quantify this relationship.

Question 3: (40 marks) The braking distance (s) required to stop an automobile is a function of velocity (v). The following experimental data was collected to quantify this relationship. v. km/hr s, m 30 5.0 45 12.3 60 21.0 75 32.9 90 47.6 120 84.7 (a) Suppose all these data can be fitted by a power relationship, i.e. s = ax vb where a and b are the fitting coefficients. Use the MATLAB built-in function fit to find the fitting curve and plot them in a red solid line by MATLAB function plot. Plot the experimental data with blue *** symbols for comparison with the fitting curve. Label the x axis as *Velocity (km/hr)', the y axis as 'Braking distance (m)', and the title as 'Power fitting'. (b) Based on the power regression, create a function M-file ("Power.m") to fit the experimental data (Do not use the MATLAB build-in functions). In the function, the input arguments are v and s, the output variable is the coefficient vector coef[a, b], i.e. function coef-power (v, s). (c) Write a script M-file ("task_c.m") to plot both the fitting curve (using a red dashed line) and the source data (using square symbols). The function M-file ("power.m") will be called to obtain the fitting data. Label the x axis as 'Velocity (km/hr)', and the y axis as *Braking distance (m)'. Include a grid over the plot area.