Problem 4 (25%) a. Assume a bus line with N stops, where distance between stops

Question

Problem 4 (25%) a. Assume a bus line with N stops, where 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 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 origin 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 of passengers. b.

Explanation / Answer

( a )

Average Speed = Total distance travelled / Total Time taken

1. Total distance travelled: There are N stops with a distance S in between each of them. Hence, total distance travelled by the bus would be ( N - 1 ) * S

2. Total time taken: There are 3 parts of time taken

a. Time for boarding/alighting of passengers at N stops = N * P * T

b. Time in accleration/deceleration = ( v / a ) + ( v / a )............where v is free flow speed and a is the acceleration/deceleration rate.

c. Time in between when there is free flow speed = ( S - ( v * v / ( a ) ) / v..........Free flow speed is maintained in between each stop except for the distance it is acclerating/decelerating.

Hence. Total time taken = ( NPT ) + ( N - 1 ) [ ( 2v/a ) + ( S/v - v/a ) ] = ( NPT ) + ( (v/a) + (S/v) ) * ( N - 1 )

Hence, Average Speed of the bus = [ ( N - 1 ) * S ] / [ ( NPT ) + ( N - 1 ) * ( (v/a) + (S/v) )

( b )

If passengers are spread uniformly along the bus route and every passenger's destination is last stop, with walking speed of passengers being u.

Travel time for first passenger at first stop would be = ( N - 1 ) * S / u

Travel time for second passenger at second stop would be = ( N - 2 ) * S / u

And similarly for other passengers till Nth stop.

Addition of all these times with a ration to N would be the average travel time.

Hence, Average travel time = ( S / u * N ) * ( N * ( N - 1 ) / 2 ) = [ ( N - 1 ) * S ] / [ ( 2 * u ) ]

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.