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Question

A point traversed half of the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time and with velocity v2 for the other half of the time. The mean velocity of the point averaged over the whole time of motion is

A
v0+v1+v23
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B
2v0+v1+v23
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C
v0+2v1+2v23
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D
2v0(v1+v2)(2v0+v1+v2)
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Solution

The correct option is D 2v0(v1+v2)(2v0+v1+v2)
Let 2S be the total distance travelled
For first half of the journey
S=v0×t1 (where t1 is the time taken to complete half of the distance)
For the remaining part of the journey we can say,
v1t+v2t=S

t=Sv1+v2
Total time =t1+2t
Mean velocity =Total displacementTotal time
=2S(Sv0)+2(Sv1+v2)
=2(1v0)+(2v1+v2)
=2v0(v1+v2)(2v0+v1+v2)

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