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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/s
Let 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 =ss3=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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