A person travels along a straight road for half the distance with velocity V₁ and the remaining half distance with velocity V₂ the average velocity is given by

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$v_{1} v_{2}$

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

${(\frac{v_{2}}{v_{1}})}^{2}$

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

answer is D.

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Detailed Solution

$V_{avg} = \frac{n}{\frac{1}{v_{1}} + \frac{1}{v_{2}} + \dots . . + \frac{1}{v_{n}}} .$

Given n = 2
$v_{avg} = \frac{2}{\frac{1}{v_{1}} + \frac{1}{v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

Alternate solution:

$v_{avg} = \frac{S_{1} + S_{2}}{t_{1} + t_{2}} = \frac{S / 2 + S / 2}{\frac{S / 2}{V_{1}} + \frac{S / 2}{V_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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