Question

A bus on a straight road starts from rest at a bus stop and accelerates at 2 m/s2 until it
reaches a speed of 40 m/s. Then the bus travels for 30 s at a constant speed in the same
direction until the driver sees the next bus stop in the distance. The driver applies the
brakes, stopping the bus in a uniform manner in 10 s.
a. Plot a rough v vs t graph for the entire trip. (Hint: There are 3 segments with
different accelerations.)
b. What is the acceleration of the bus at t = 10 s? t = 40 s? t = 55 s?
c. How long does the bus take to travel from the first bus stop to the second bus stop?
d. What is the average velocity of the bus during the trip?

Answer 1

in general
v = Vi + a t
x = Xi + Vi t + (1/2) a t^2
Phase 1, stop 1 to stop 2
v= 0 + 2 t = 40
x = 0 + 0 + (1/2) 2 t^2
so
t = 20
x = 400 meters
Phase 2 stop 2 to stop 3
Vi = 40
Xi = 400
t = 30 so 50 seconds so far
v = 40 constant
x = 400 + 40*30 = 1600 at stop 3
Phase 3 , stop 3 to end
t = 10 so 60 seconds for trip
v = 0 = 40 + a (10) so a = -4 m/s^2
x = 1600 + 40*10 - (1/2)4*100 = 1800 at end