A) \[v=\sqrt{{{v}_{1}}{{v}_{2}}}\]
B) \[v=\frac{{{v}_{1}}+{{v}_{1}}}{2}\]
C) \[v=\frac{{{v}_{1}}}{{{v}_{2}}}\]
D) \[\frac{2}{v}=\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}\]
Correct Answer: D
Solution :
Average velocity \[=\frac{total\text{ }distance\text{ }travelled}{total\text{ }time\text{ }taken}\] Let the total distance\[=d\]. \[\therefore \] \[v=\frac{d}{\frac{d}{2{{v}_{1}}}+\frac{d}{{{v}_{2}}}}\] \[v=\frac{d}{\frac{d}{2}\left( \frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}} \right)}\] Or \[v=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] Or \[\frac{{{v}_{1}}+{{v}_{2}}}{{{v}_{1}}{{v}_{2}}}=\frac{2}{v}\] Or \[\frac{1}{{{v}_{1}}}+\frac{1}{{{v}_{2}}}=\frac{2}{v}\]
You need to login to perform this action.
You will be redirected in
3 sec
