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Velocity(Speed with Direction)

If a car cove...

Question

If a car covers $\frac{2}{5^{t h}}$ of the total distance with $v_{1}$ speed and $\frac{3}{5^{t h}}$ distance with $v_{2}$ then average speed:

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is D $\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$
Time taken to cover $\frac{2}{5} t h$ distance: $t_{1} = \frac{2}{5} \frac{s}{v_{1}} = \frac{d i s t a n c e}{v e l o c i t y}$ where s is total distance
Time taken to cover $\frac{3}{5} t h$ distance: $t_{1} = \frac{3}{5} \frac{s}{v_{2}}$
Average speed $= \frac{t o t a l d i s t a n c e}{t o t a l t i m e}$
$V_{m g} = \frac{s}{t_{1} + t_{2}}$
$= \frac{s}{\frac{2 s}{5 v_{1}} + \frac{3 s}{5 v_{2}}}$
$= \frac{5 v_{1} v_{2} s}{s (2 v_{2} s + 3 v_{1} s)}$
$\frac{5 v_{1} v_{2}}{3 v_{1} + 2 v_{2}}$

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