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] \[\text{Average}\,\text{speed}=\frac{\text{Total distance traveled}}{\text{Total time taken}}\] |
\[=\frac{x}{{{t}_{1}}+{{t}_{2}}}\] |
\[=\frac{x}{\frac{(2/5)x}{{{v}_{1}}}+\frac{(3/5)x}{{{v}_{2}}}}=\frac{5{{v}_{1}}{{v}_{2}}}{2{{v}_{2}}+3{{v}_{1}}}\] |
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