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Q.

A car travels from the place A to B with a speed $V_{1}$ . During its return journey from B to A its speed is $V_{2}$ . Then the average speed in complete journey is

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a

$2 \frac{V_{1} V_{2}}{V_{1} + V_{2}}$

b

$\frac{V_{1} {+V}_{2}}{2}$

c

$2 \frac{(V_{1} + V_{2})}{V_{1} V_{2}}$

d

$\sqrt{\frac{V_{1} + V_{2}}{2}}$

answer is A.

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Detailed Solution

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$V_{a v e} = \frac{Totaldistance}{Totaltime}$

$= \frac{s_{1} + s_{2}}{t_{1} + t_{2}} = \frac{s + s}{\frac{s}{v_{1}} + \frac{s}{v_{2}}}$

$= \frac{2 s}{s [\frac{1}{v_{1}} + \frac{1}{v_{2}}]} = \frac{{2v}_{1} v_{2}}{(v_{1} + v_{2})}$

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