question_answer

A person completes half of its journey with  speed\[{{v}_{1}}\]and rest half with speed \[{{v}_{2}}.\]The average speed of the person is:

A) \[v=\frac{1}{2}({{v}_{1}}+{{v}_{2}})\]

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

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

D) \[v=\sqrt{{{v}_{1}}{{v}_{2}}}\]

Correct Answer: B

Solution :

 \[\text{Aerage}\,\text{speed}\,\text{=}\,\frac{\text{total}\,\text{distace}\,\text{travelled}}{\text{total}\,\text{time}\,\text{takent}}\] Time taken for \[OA=\frac{x}{{{v}_{1}}}\] Time taken for \[AB=\frac{x}{{{v}_{2}}}\] Total time \[=\frac{x}{{{v}_{1}}}+\frac{x}{{{v}_{2}}}\]