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A train starting from rest at one station, acclerates uniformly and attains a speed v after sometime. After travelling at this speed for sometime, it retards uniformly and stop at the next station. If R be the uniform resistance of the given track and the duration of the uniform motion is just half the total journey time, the average power supplied by the train engine is:- a) (vR)/2 b) (3vR)/2 c) (3vR)/4 d) (vR)/4
Asked by acv27joy | 16 Sep, 2018, 12:47: PM
Let t be the time taken to complete the total journey.
It is given that half of the time train travels with uniform speed v.

Hence distance S1 travelled in half of the total time is given by,  S1 = v×(t/2) ...............(1)

When the train was moving with uniform acceleration train starts from rest and attains a speed v after some time.
Hence average speed during accelerated movement is v/2.

Similarly when retardataion started from speed v to zero, average speed is again v/2.

Hence for remaining half of the time train moves with average speed v/2 and the distance S2 travelled is given by,

S2 = (v/2)×(t/2)  .......................(2)

from (1) and (2), total distance S travelled is given by,  S  = S1+S2 = v×(t/2) + (v/2)×(t/2) = (3/4)×v×t .................(3)

average speed = total-distane / time = { (3/4)×v×t } / t =  (3/4)×v ......................(4)

average power = average-speed × average-Resistance  = (3/4)×v×R
Answered by Thiyagarajan K | 16 Sep, 2018, 04:23: PM

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