A) \[0,{{v}_{1}}+{{v}_{2}}\]
B) \[\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}},0\]
C) \[{{v}_{1}}+{{v}_{2}},0\]
D) \[{{v}_{1}}-{{v}_{2}},\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]
Correct Answer: B
Solution :
Average speed \[=\frac{total\text{ }distance}{total\text{ }time\text{ }taken}\] \[=\frac{x+x}{{{t}_{1}}+{{t}_{2}}}=\frac{2x}{\frac{x}{{{v}_{1}}}+\frac{x}{{{v}_{2}}}}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] Average velocity \[=\frac{total\text{ }displacement}{total\text{ }time\text{ }taken}\] \[=\frac{x+(-x)\_}{{{t}_{1}}+{{t}_{2}}}=\frac{0}{{{t}_{1}}+{{t}_{2}}}=0\]
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