Question

Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken is 1:8:1 and the maximum speed attained is 60km/hr, then what is the average speed over the whole journey?

Answer 1

Let it accelerates with say ‘a’ in time ‘x’ then it reaches a velocity ‘v’ and continues motion for time ‘8x’ abd finally then retards with ‘b’ in time ‘x’.

v = 0 + ax

=> v = ax

=> 60 = ax

=> a = 60/x

And,

0 = v – bx

=> b = 60/x

Distance covered in time of acceleration,

S1 = 0 + ½ at2

=> S1 = ½ ax2 = ½ × 60/x × x2 = 30x

Distance covered while moving with constant velocity is,

S2 = vt = 60 × 8x = 480x

Distance covered in time of retardation,

02 = v2 - 2bS3

=> S3 = 602/(2 × 60/x)

=> S3 = 30x

So, total distance = 30x + 480x + 30x = 540x

Total time = x + 8x + x = 10x

So, average velocity = 540x/10x = 54 km/h