A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by

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A person travelling on a straight line moves with a uniform velocity v₁ for a distance x and with a uniform velocity v₂ for the next equal distance. The average velocity v is given by

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

$v = \sqrt{v_{1} v_{2}}$

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

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

answer is C.

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let the total distance travelled =2x

time taken during first phase = $\frac{x}{v_{1}}$

time taken during second phase = $\frac{x}{v_{2}}$

Average velocity is given by $v_{avg} = \frac{2 x}{\frac{x}{v_{1}} + \frac{x}{v_{2}}}$

$\Rightarrow \frac{2}{v_{avg}} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

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