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Question

# A particle travels half the distance with a velocity of 6 m/s. The remaining half distance is covered with a velocity of 4 m/s for half the time and with a velocity of 8 m/s for the rest of the half time. What is the velocity of the particle averaged over the whole time of motion?

A
9 m/s
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B
6 m/s
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C
5.35 m/s
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D
5 m/s
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Solution

## The correct option is B 6 m/sLet the particle travels a distance 2d.Covering the first half:The particle travels the first half (distance = d) with a velocity 6 m/s.Thus, the time taken (t1) to cover d distance is d6. ∴t1=d6Covering the second half:Let 2t is the time taken to cover the distance d.The particle moves with a velocity 4 m/s for time t and then it moves with a velocity 8 m/s for time t.Thus, the total distance covered in 2t is (4×t)+(8×t)=12tSo, 12t=d ⇒2t=d6Average velocity=Total distanceTotal time=2dt1+2t=2dd6+d6=2dd3=6 m/s

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