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Question

# A body traveling along a straight line traversed first one third of the total distance with a velocity 4 m/s. The remaining part of the distance was covered with a velocity 2 m/s for half the time and with velocity 6 m/s for the other half of time. The average velocity over the whole time of motion is

A
5 m/s
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B
4 m/s
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C
4.5 m/s
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D
3 m/s
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Solution

## The correct option is B 4 m/sLet total distance =s Distance covered with a velocity of 4 m/s=s3 Let the time taken to cover first one third distance =t1, then t1=s34=s12 Now let t2 be the time for the rest two journeys. Distance covered in rest of the two journeys =s−s3=2s3 Since half of the remaining distance is covered at 2 m/s and half at 6 m/s. Therefore 2s3=2t2+6t2=8t2 ∴t2=2s24=s12 Total time taken to cover rest of the two journeys =2t2=s6 ∴ Average velocity =total displacementtotal time =st1+2t2=ss12+s6=12×612+6=4 m/s

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