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Average and Instaneous Power

A particle co...

Question

A particle covers half of its total distance with speed, $v_{1}$ and the rest half distance with speed, $v_{2}$ . Its average speed during the complete journey is

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is C $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
$V_{a v} = \frac{S + S}{\frac{S}{V_{1}} + \frac{S}{V_{2}}} = \frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

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