InterviewSolution
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InterviewSolution
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8. Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finallyretards uniformly to come to rest. If the ratio of the time taken be 1 8 1and the maximum speed attained be60 km/h, then what is the average speed over the whole journey?A) 48 km/hB) 52 km/hC) 54 km/hD) 56 km/h |
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Answer» Let it accelerates with say ‘a’ in time ‘x’ then it reaches a velocity ‘v’ and continues motion for time ‘8x’ abd finally then retards with ‘b’ in time ‘x’.v = 0 + ax=> v = ax=> 60 = ax=> a = 60/xAnd,0 = v – bx=> b = 60/xDistance covered in time of acceleration,S1= 0 + ½ at2=> S1= ½ ax2= ½ × 60/x × x2= 30xDistance covered while moving with constant velocity is,S2= vt = 60 × 8x = 480xDistance covered in time of retardation,02= v2- 2bS3=> S3= 602/(2 × 60/x)=> S3= 30xSo, total distance = 30x + 480x + 30x = 540xTotal time = x + 8x + x = 10xSo, average velocity = 540x/10x = 54 km/h |
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