A metro train starts from rest and in 5 s achieves 108 km $h^{- 1}$ . After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 390 m, find total time of travelling.

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12 s

15.3 s

9 s

17 s

answer is D.

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Detailed Solution

Velocity time graph is

$S_{1} = \frac{1}{2} vt = \frac{1}{2} (108 \times \frac{5}{18}) 5 = 75 m t_{1} = 5 \sec$

$S_{2}$ =390-75-45=270m

$t_{2} = \frac{270}{30} = 9 \sec$

$s_{3} = \frac{1}{2} \times 30 \times t_{3} = 45$

$t_{3} = \frac{45 \times 2}{30} = 3 \sec$

Total time = 9+5+3=17 sec

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