A passenger travels along the straight road for half the distance with velocity, $v_{1}$ and the remaining half distance with velocity, $v_{2}$ . Then average velocity is given by

v_{1} v_{2}

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

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

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

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Solution

The correct option is D $\frac{2 v_{1} v_{2}}{(v_{1} + v_{2})}$
For the first half distance $= x$ , velocity $= v_{1}$ , time $= t_{1} = \frac{x}{v_{1}}$
For the second half distance $= x$ , velocity $= v_{2}$ , time= $t_{2} = \frac{x}{v_{2}}$
Mean velocity $= \frac{x + x}{t_{1} + t_{2}} = \frac{2 x}{\frac{x}{v_{1}} + \frac{x}{v_{2}}} = \frac{2 v_{1} v_{2}}{{v_{1} + v}_{2}}$

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