A particle travels half the distance with velocity u. The remaining part of the distance is covered with velocity $v_{1}$ for the first half time and $v_{2}$ for the remaining half time. The average velocity of the particle during the complete motion is

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

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

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

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

answer is B.

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Detailed Solution

When time intervals are equal, then distance are equal

$v_{a v} = \frac{2 u v_{m}}{u + v_{m}} = \frac{2 u (\frac{v_{1 +} v_{2}}{2})}{u + (\frac{v_{1} + v_{2}}{2})} = \frac{2 u (v_{1} + v_{2})}{2 u + v_{1} + v_{2}}$

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