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Question

A particle travelling in a straight path in the same direction covers the first half of the distance with a velocity v1 and the second half of the distance with two different velocities v2 and v3 in equal intervals of time. The average velocity of the particle for the entire journey is

A
(v1+v2)v3v1+v2+v3
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B
(v1+v3)v2v1+v2+v3
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C
2v1(v2+v3)v1+v2+v3
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D
2v1(v2+v3)2v1+v2+v3
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Solution

The correct option is D 2v1(v2+v3)2v1+v2+v3
Let the total displacement of the body be 2S and let t1 be the time taken to cover the first half.
During the second half, let the time of travel be 2t, so that it travels with v2 and v3 velocities in time t each.
Then, average velocity =2St1+2t
Here, t1=Sv1 and (v2+v3)t=S
i.e t=S(v2+v3)

vav=2SSv1+2(Sv2+v3)=21v1+2v2+v3
=2v1(v2+v3)2v1+v2+v3

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