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Displacement

A particle tr...

Question

A particle travels half of total distance with speed $v_{1}$ and next half with speed $v_{2}$ along a straight line. Find out the average speed of the particle?

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

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\frac{v_{1} - v_{2}}{2 v_{1} v_{2}}

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Solution

The correct option is B $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
Suppose a particle travel "2x" distance linearly
hence in time $t_{1}$ he can travel "x" distance and in time $t_{2}$ he can travel next "x" distance.
so from the definition of average speed which is equals to $\frac{total distance traveled}{total time taken}$ = $\frac{2 x}{\frac{x}{v_{1}} + {\frac{x}{v}}_{2}}$ = $\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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A particle travels half of total distance with speed v1 and next half with speed v2 along a straight line. Find out the average speed of the particle?

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