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 :
Average speed\[=\frac{\text{total}\,\,\text{distance}\,\,\text{travelled}}{\text{total}\,\,\text{time}\,\,\text{taken}}\] Time taken for\[OA=\frac{x}{{{v}_{1}}}\] Time taken for\[AB=\frac{x}{{{v}_{2}}}\] Total time\[=\frac{x}{{{v}_{1}}}+\frac{x}{{{v}_{2}}}\] \[\therefore \]Average speed\[=\frac{2x}{\frac{x}{{{v}_{1}}}+\frac{x}{{{v}_{2}}}}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]You need to login to perform this action.
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