A particle traversed along a straight line for first half time with velocity V₀. For the remaining part, half of the distance is traversed with velocity V₁ and other half distance with velocity V₂. Find the mean velocity of the particle for the total journey.

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$\frac{v_{0} + 2 v_{1} v_{2}}{2 (v_{1} + v_{2})}$

$\frac{2 v_{0} (v_{1} + v_{2})}{v_{1} + v_{2} + 2 v_{0}}$

$\frac{v_{1} + v_{2}}{2}$

$\frac{v_{0} (v_{1} + v_{2}) + 2 v_{1} v_{2}}{2 (v_{1} + v_{2})}$

answer is B.

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Detailed Solution

For second half $= \frac{s + s}{\frac{s}{v_{1}} + \frac{s}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Average velocity $= \frac{v_{0} + \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}}{2}$
$= \frac{v_{0} [v_{1} + v_{2}] + 2 v_{1} v_{2}}{2 [v_{1} + v_{2}]}$

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