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.

Asked by PRINCE SHARMA | 16th Jun, 2013, 09:52: PM

Expert Answer:

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

Answered by  | 16th Jun, 2013, 10:14: PM

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