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A car travelling on a straight track moves with a uniform velocity $V_{1}$ for half of the time and with a uniform velocity $V_{2}$ for rest of the time. The average velocity is

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

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

${(\frac{1}{v_{1}} + \frac{1}{v_{2}})}^{- 1}$

$2 {(\frac{1}{v_{1}} + \frac{1}{v_{2}})}^{- 1}$

answer is B.

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Detailed Solution

$V_{avg} = \frac{v_{1} t_{1} + v_{2} t_{2}}{t_{1} + t_{2}}$

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

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

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