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Finding Average Velocity

A body covers...

Question

A body covers one third of the distance with speed $V_{1}$ and two third of the distance with speed $V_{2}$ . The average speed of the body is:

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

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\frac{V_{1} + V_{2}}{2}

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\frac{3 V_{1} V_{2}}{2 V_{1} + V_{2}}

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\frac{3 V_{1} V_{2}}{V_{1} + 2 V_{2}}

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Solution

The correct option is C $\frac{3 V_{1} V_{2}}{2 V_{1} + V_{2}}$
time taken is t
$t = \frac{\frac{x}{3}}{V_{1}} + \frac{\frac{2 x}{3}}{V_{2}}$
average speed is $v = \frac{x}{t}$

$V_{a v g} = \frac{x}{\frac{x}{3 v_{1}} + \frac{2 x}{3 V_{2}}} = \frac{3 V_{1} V_{2}}{V_{2} + 2 V_{1}}$

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List - I	List - II
a) A body covers first half of distance with a speed $V_{1}$ and second half of distance with a speed $V_{2}$	e) Average velocity is $\sqrt{\frac{g h}{2}}$
b) A body covers first half of the time with a speed $V_{1}$ and second half of the time with a speed $V_{2}$	f) Average speed is $\frac{v_{1} + v_{2}}{2}$
c) A body is projected vertically up from ground with certain velocity.Considering its total motion,	g) Average speed is $\frac{2 V_{1} V_{2}}{V_{1} + V_{2}}$
d) A body freely is released from a height h	h) Average velocity is zero

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