# A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m

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A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.

(a) 12.2s

(b) 15.3s

(c) 9s

(d) 17.2 s

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Correct option (d) 17.2s

Explanation:

Given : u = 0, t = 5 sec, v = 108 km/hr = 30m/s

By eqn of motion

v = u + at

or a = c/t = 30/5 = 6m/s2 [u = 0]

S1 = 1/2at2

= 1/2 x 6 x 52 = 75

Distance travelled in first 5 sec is 75m.

Distance travelled with uniform speed of 30m/s is S2

395 = S1 + S2 + S3

395 = 75 + S2 + 45

∴ S2 = 395 – 120 = 275 m

Time taken to travel 275 m = 275/30 = 9.2sec

For retarding motion, we have

02 – 302 = 2(– a) × 45

We get, a = 10 m/s2

Now by, S =  ut + 1/2at2

45 = 30t + 1/2(-10)t2

45 = 30t - 5t2

on solving we get, t = 3 sec

Total time taken = 5 + 9.2 + 3

= 17.2 sec.