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Q.

A person completes half of his journey with speed $υ_{1}$ and rest half with speed $υ_{2}$ . The average speed of the person is

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a

$υ = \frac{2 υ_{1} υ_{2}}{υ_{1} + υ_{2}}$

b

$υ = \sqrt{υ_{1} υ_{2}}$

c

$υ = \frac{υ_{1} + υ_{2}}{2}$

d

$υ = \frac{υ_{1} υ_{2}}{υ_{1} + υ_{2}}$

answer is A.

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Detailed Solution

$\begin{aligned} v_{a v} = \frac{(d_{1} + d_{2})}{(\frac{d_{1}}{v_{1}} + \frac{d_{2}}{v_{2}})} = \frac{(\frac{d}{2} + \frac{d}{2})}{(\frac{d / 2}{v_{1}} + \frac{d / 2}{v_{2}})} \\ \Rightarrow v_{a v} = \frac{2}{(\frac{1}{v_{1}} + \frac{1}{v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}} \end{aligned}$

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