A man travels along a straight line. He covers the first half distance with constant velocity $v_{1}$ and the next half distance with constant velocity $v_{2} .$ The average velocity of man will be :

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

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

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{(v_{1} v_{2})}^{1 / 2}

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

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Solution

The correct option is C $v = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Let Total distance = D
For, distance , $\frac{D}{2}, V = V_{1}$
$t_{1} = \frac{D / 2}{V_{1}} = D / 2 v_{1}$
For wxt $\frac{D}{2}, V = V_{2}$
$t_{2} = \frac{D / 2}{V_{2}} = D / 2 v_{2}$
average velocity = $\frac{T o t a l d i s t a n c e t r a v e l l e d}{T o t a l t i m e}$
$\frac{D}{\frac{D}{2 V_{1}} + \frac{D}{2 V_{2}}} = \frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$
average velocity = $\frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$

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