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Q.

A body covers the first one-third of the distance with a velocity ‘a’, the second one-third of the distance with a velocity ‘b’ and the remaining with a velocity ‘c’. The average velocity is

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a

\frac{a b + b c + c a}{3}

b

\frac{1}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}

c

\frac{3 a b c}{a b + b c + c a}

d

\frac{a + b + c}{3}

answer is B.

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Detailed Solution

$V_{A v g} = \frac{\frac{S}{3} + \frac{S}{3} + \frac{S}{3}}{\frac{S}{3 a} + \frac{S}{3 b} + \frac{S}{3 c}}$

$\frac{\frac{3 S}{3}}{\frac{S}{3} [\frac{b c + c a + a b}{a b c}]}$

$\begin{matrix} V_{A v g} = \frac{3 a b c}{b c + c a + a b} o r^{} \\ = \frac{3 a b c}{a b + b c + c a} \end{matrix}$

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A body covers the first one-third of the distance with a velocity ‘a’, the second one-third of the distance with a velocity ‘b’ and the remaining with a velocity ‘c’. The average velocity is