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Question

Between two stations, a train accelerates uniformly at first, then moves with constant speed and finally retards uniformly. If the ratios of time taken are 2:1:2 and the greatest speed is 10 km/hr, find the average speed over the whole journey.

A
6 km/hr
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B
9 km/hr
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C
4.5 km/hr
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D
3 km/hr
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Solution

The correct option is A 6 km/hr
Let, the time taken to travel second part of the journey be t, where the train accelerates with constant acceleration.

Since, the ratio of the times are 2:1:2 so, the time taken to travel the part of the journey is 2t and time taken to the third part of the journey is 2t.

Below, given vt graph shows the motion.


Average speed of the journey,

=Area under v-t curvetotal time

=12×10×2t+10×t+12×10×2t5t

=30t5t=6 km/h

Hence, (A) is the correct answer.

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