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Time and Speed

A vehicle tra...

Question

A vehicle travels half the distance L with speed $v_{1}$ and the other half with speed $v_{2},$ then its average speed is

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

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

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

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

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Solution

The correct option is C $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
$Avg. speed = \frac{Total distance traveled}{total time taken}$
$⟹ \frac{L}{\frac{\frac{L}{2}}{v_{1}} + \frac{\frac{L}{2}}{v_{2}}} = \frac{L}{\frac{L}{2 v_{1}} + \frac{L}{2 v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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A vehicle travels half the distance L with speed v1 and the other half with speed v2, then its average speed is

The correct option is C 2v1v2v1+v2Avg. speed=Total distance traveledtotal time taken⟹LL2v1+L2v2=LL2v1+L2v2=2v1v2v1+v2

A vehicle travels half the distance L with speed $v_{1}$ and the other half with speed $v_{2},$ then its average speed is

The correct option is C $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
$Avg. speed = \frac{Total distance traveled}{total time taken}$
$⟹ \frac{L}{\frac{\frac{L}{2}}{v_{1}} + \frac{\frac{L}{2}}{v_{2}}} = \frac{L}{\frac{L}{2 v_{1}} + \frac{L}{2 v_{2}}} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$