Between two stations, a train accelerates uniformly at first, then moves with a constant speed and finally retards uniformly. If the ratio of the time taken 1:8:1 and the greatest speed is 60km/hr , Find the average speed over the whole journey.

greatest speed is achieved when the car will be at the end of its acceleration time, and moves with constant speed, v = 60kmph.

let the respective time slots for each period be t:8t:t

let acceleration be a

thus if initial velocity = 0

then using first equation of motion:

v = 60 = a.t

distance travelled whilr this time: s1 = 1/2 a.t² = 1/2 60t = 30t

 

distance traveled in next constant sped slot:

 

s2 = 60.8t = 240t

 

let retarding be at rate r

 

thus using first eq of motion:

 

60 = rt

 

distance travelled in this slot:

 

s3 = (60)²/2r = 30t

 

thus average speed = total distance / total time = (30t+240t+30t)/9t = 33.33 kmph