A car moves from X to Y with a uniform speed v₁ and returns to Y with a uniform speed v₂ . avera

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2.Motion in Straight Line

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A car moves from $X$ to $Y$ with a uniform speed $v_1$ and returns to $Y$ with a uniform speed $v_2$ . The average speed for this round trip is

A

$\bar v = \frac{{{v_1} + {v_2}}}{2}$

B

$\bar v =\sqrt {{v_1}{v_2}} $

C

$\frac{{2}}{{\bar v}} =\frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}$

D

$\frac{{1}}{{\bar v}} =\frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}$

(AIPMT-2007) (NEET-2019)

Solution

Average speed $=\frac{\text { Total distance }}{\text { Total time }}$

$\bar v=\frac{2 d}{\frac{d}{v_{1}}+\frac{d}{v_{2}}}$

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

Standard 11

Physics

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