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Question 1 (9 marks): Vehicle 2 is following Vehicle 1 in a single-lane highway where no passing is allowed. Their initial speeds at time = 0 are 45 ft/s. The initial positions of Vehicle 1 and Vehicle 2 at time = 0 are 150 ft and 0 ft, respectively. The lead vehicle (Vehicle 1) suddenly decelerates at a constant rate of 4.5 ft/s2 until it completely stops. (3) (3 marks) Using the GM] car-following mode], calculate the acceleration, speed and position of both vehicles for all time intervals until both vehicles stop (if the speed of Vehicle 2 is less than 0.01 ft/s, assume that Vehicle 2 stops). Driver's perception-reaction time (At) is l s and the sensitivity parameter (or) is 0.37 s'l. Show your sample calculation for time = 1 s. (b) (3 marks) Plot the trajectories of Vehicles 1 and 2 in a time-space diagram. Show the distance in ft in yaxis (direction of movement points upwardT) and the time in seconds in xaxis. Comment on how the spacing between the two vehicles changes over time. (c) (3 marks) Repeat the calculation in part (a) using the sensitivity parameters (or) is 0.74 s'1 and plot the trajectories of Vehicles 1 and 2 in a timespace diagram. Comment on how Vehicle 2's car-following behavior changes compared to the result in part (a). Explain how the sensitivity parameter affected Vehicle 2's car-following behavior