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Q.

If a car covers $2 / 5 t h$ of the total distance with $v_{1}$ speed and $3 / 5 t h$ distance with $v_{2},$ then average speed is:-

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a

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

b

$\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$

c

$\frac{1}{2} \sqrt{v_{1} v_{2}}$

d

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

answer is D.

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Detailed Solution

The average speed $= \frac{\frac{2 x}{5} + \frac{3 x}{5}}{\frac{2 x / 5}{v_{1}} + \frac{3 x / 5}{v_{2}}} = \frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$

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