A boy runs along a straight path for the first half distance with a velocity $v_{1}$ and the second half distance with a velocity $v_{2}$ . The mean velocity V is given by

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

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

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V = \sqrt{v_{1} v_{2}}

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_{1} +_{2}

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Solution

The correct option is A $\frac{2}{V} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
$V_{a v g} = \frac{t o t a l d i s t a n c e}{t o t a l t i m e}$
Total distance = d + d = 2d
time = $t_{1} + t_{2}$
$t_{1} = \frac{d}{v_{1}} t_{2} = \frac{d}{v_{2}}$
$∴ V_{a v g} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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A boy runs along a straight path for the first half distance with a velocity v1 and the second half distance with a velocity v2. The mean velocity V is given by

The correct option is A 2V=1v1+1v2Vavg=total distancetotal time Total distance = d + d = 2d time = t1+t2 t1=dv1t2=dv2 ∴Vavg=2v1v2v1+v2

A boy runs along a straight path for the first half distance with a velocity $v_{1}$ and the second half distance with a velocity $v_{2}$ . The mean velocity V is given by

The correct option is A $\frac{2}{V} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
$V_{a v g} = \frac{t o t a l d i s t a n c e}{t o t a l t i m e}$
Total distance = d + d = 2d
time = $t_{1} + t_{2}$
$t_{1} = \frac{d}{v_{1}} t_{2} = \frac{d}{v_{2}}$
$∴ V_{a v g} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$