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Q.

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

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a

54 km/h

b

50 km/h

c

48 km/h

d

60 km/h

answer is C.

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Detailed Solution

Let s₁, s₂ and s₃ be the respective distances. Then
$s_{1} = (\frac{60 + 0}{2}) t, s_{2} = 60 (8 t) and s_{3} = (\frac{60 + 0}{2}) t$
$\begin{array}{l} ∴ Average speed = \frac{s_{1} + s_{2} + s_{3}}{t + 8 t + t} \\ = \frac{30 t + 480 t + 30 t}{10 t} = \frac{540 t}{10 t} \\ = 54 km / h \end{array}$

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