question_answer

If a car covers 2/5th of the total distance with \[{{v}_{1}}\] speed and 3/5th distance with \[{{v}_{2}},\] then average speed is

A) \[\frac{1}{2}\,\sqrt{{{v}_{1}}{{v}_{2}}}\]

B) \[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]

C) \[\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]

D) \[\frac{5{{v}_{1}}{{v}_{2}}}{3{{v}_{1}}+2{{v}_{2}}}\]

Correct Answer: D

Solution :

[d] \[\text{Average}\,\text{speed}=\frac{\text{Total distance traveled}}{\text{Total time taken}}\]

\[=\frac{x}{{{t}_{1}}+{{t}_{2}}}\]

\[=\frac{x}{\frac{(2/5)x}{{{v}_{1}}}+\frac{(3/5)x}{{{v}_{2}}}}=\frac{5{{v}_{1}}{{v}_{2}}}{2{{v}_{2}}+3{{v}_{1}}}\]