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Velocity in 2D

A particle tr...

Question

A particle traversed half of the distance with a velocity $v_{0}$ . The half of remaining part of the distance was traveled with velocity $v_{1}$ and second half of remaining part by velocity $v_{2}$ . The average velocity of the particle, during the complete time of motion is:

\frac{v_{0} + v_{1} + v_{2}}{3}

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\frac{2 v_{0} + v_{1} + v_{2}}{3}

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\frac{v_{0} + 2 v_{1} + 2 v_{2}}{3}

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\frac{4 v_{0} v_{1} v_{2}}{v_{0} (v_{1} + v_{2}) + 2 v_{1} v_{2}}

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Solution

The correct option is D $\frac{4 v_{0} v_{1} v_{2}}{v_{0} (v_{1} + v_{2}) + 2 v_{1} v_{2}}$
Avg speed $= \frac{t o t a l d i s t a n c e}{t o t a l t i m e}$
Total distance $= x$
Total time $= \frac{x}{2} V_{0} + \frac{x}{4} V_{1} + \frac{x}{4} V_{2}$

Hence, $V_{a v g} = \frac{4 V_{0} V_{1} V_{2}}{V_{0} (V_{1} + V_{2}) + 2 V_{1} V_{2}}$

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⟨ v ⟩ = \frac{x v_{0} (v_{1} + v_{2})}{2 v_{0} + v_{1} + v_{2}}

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