A body covers one-third of the distance with a velocity $v_{1},$ the second one-third of the distance with a velocity $v_{2}$ and the remaining distance with a velocity $v_{3} .$ The average velocity is

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$\frac{v_{1} + v_{2} + v_{3}}{3}$

$\frac{3 v_{1} v_{2} v_{3}}{v_{1} v_{2} + v_{2} v_{3} + v_{3} v_{1}}$

$\frac{v_{1} v_{2} + v_{2} v_{3} + v_{3} v_{1}}{3}$

$\frac{v_{1} v_{2} v_{3}}{3}$

answer is B.

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Detailed Solution

$t_{1} = \frac{S / 3}{v_{1}}, t_{2} = \frac{S / 3}{v_{2}}, t_{3} = \frac{S / 3}{v_{3}}$

$v_{a v} = \frac{S}{t_{1} + t_{2} + t_{3}} = \frac{3 v_{1} v_{2} v_{3}}{v_{1} v_{2} + v_{2} v_{3} + v_{3} v_{1}}$

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