Problem 5 (30%) da. Assume a bus line with N stops, where the distance between stops is S. Free flow speed of the bus is v, with acceleration and deceleration, a. P passengers per stop are boarding and alighting, and the time needed for a passenger to board or alight is T seconds. What is the average speed of a bus? Following on part (a), assume the origins of passengers are spread uniformly along the bus route. The destination of all passengers is the last stop. The walking speed of passengers is u. Determine the average travel time (walking + in-vehicle) of passengers. Simplify the above equation when N is large enough (approximating N-1/2 by N-1). Consider now that you can decide on S, where you replace N=L/S (L is the length of the route). Find the value of S that minimises the travelling time of the passengers. In the same setting as (c), assume that some passengers do not go to the terminal but alight before. Explain if your answer from (c) would increase or decrease and why. If you need to assume other variables and parameters to solve this problem, clearly state that in your report and explain the reason