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Q.

A metro train starts form rest and in five seconds achieves a speed 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.

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a

17.2 sec

b

15.3 s

c

9 s

d

12.2 sec

answer is A.

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Detailed Solution

I-part

$V = u + a t \to a = 6 m / \sec^{2}$

$S = u t + \frac{1}{2} a t^{2} \to S_{1} = 75 m$

II-Part

$\begin{array}{l} S = S_{1} + S_{2} + S_{3} \\ 395 = 75 + S_{2} + 45 \\ S_{2} = 275 m \\ t = \frac{S_{2}}{V_{2}} \\ t = \frac{275}{30} = 9.16 \sec \\ = 9.2 \sec \end{array}$

III-Part

$u = 108 \times \frac{5}{18} = 30 m / \sec$

$\begin{array}{l} a = \frac{V^{2} - u^{2}}{2 S_{3}} = \frac{- 30 \times 30}{2 \times 45} \\ S_{3} = 45 m a = 10 / m / \sec^{2} \\ V = u + a t \to t = 3 \sec \\ 0 = 30 - 10 t \end{array}$

$∴$ Total time t=5+9.2+3

T=17.2 sec

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