A) \[\frac{{{v}_{1}}{{v}_{2}}}{2({{v}_{1}}+{{v}_{2}})}\]
B) \[\frac{2\,{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]
C) \[\frac{{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]
D) None of these
Correct Answer: B
Solution :
Let total distance be s and be time taken to cover distance\[\frac{s}{2}\], and \[{{t}_{2}}\] be time taken to cover rest of distance \[\frac{s}{2}\], Then, \[{{t}_{1}}=\frac{s/2}{{{v}_{1}}}\] and \[{{t}_{2}}=\frac{s/2}{{{v}_{2}}}\] Now, average speed \[{{\operatorname{v}}_{avg}}=\frac{total\,\,dis\tan ce}{total\,\,time}\] \[=\,\,\,\frac{s}{{{t}_{1}}+{{t}_{2}}}\] \[=\,\,\,\frac{s}{\frac{s/2}{{{v}_{1}}}+\frac{s/2}{{{v}_{2}}}}\] \[=\,\,\,\frac{1}{\frac{1}{2\,{{v}_{1}}}+\frac{1}{2\,{{v}_{2}}}}\] \[=\,\,\,\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]
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