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Finding Average Velocity

A motor car t...

Question

A motor car travels with a speed $v_{1}$ from A to B and returns back from B to A with a speed $v_{2}$ . The average speed of the car during its journey IS

A

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

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B

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

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C

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

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D

\sqrt{v_{1} v_{2}}

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Solution

The correct option is B $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
[Average velocity = $\frac{T o t a l d i s t a n c e}{T o t a l t i m e}$
$= \frac{s + s}{t_{1} + t_{2}} = \frac{2 s}{\frac{s}{v_{1}} + \frac{s}{v_{2}}} = \frac{2}{\frac{v_{2} + v_{1}}{v_{1} v_{2}}}$
$= \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$ ]

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