A) \[2{{V}_{1}}\left( {{V}_{0}}+{{V}_{2}} \right)/\left( {{V}_{0}}+2{{V}_{1}}+2{{V}_{2}} \right)\]
B) \[2{{V}_{0}}\left( {{V}_{0}}+{{V}_{1}} \right)/\left( {{V}_{0}}+{{V}_{1}}+{{V}_{2}} \right)\]
C) \[2{{V}_{0}}\left( {{V}_{1}}+{{V}_{2}} \right)/\left( {{V}_{1}}+{{V}_{2}}+2{{V}_{0}} \right)\]
D) \[2{{V}_{2}}\left( {{V}_{0}}+{{V}_{1}} \right)/\left( {{V}_{1}}+2{{V}_{2}}+{{V}_{0}} \right)\]
Correct Answer: C
Solution :
| [c] Let s be the total displacement, then |
| \[=\frac{s}{2}={{v}_{0}}{{t}_{2}}+\operatorname{or}\ {{t}_{1}}=\frac{s}{2{{v}_{0}}}\] |
| and \[=\frac{s}{2}={{v}_{1}}{{t}_{2}}+{{v}_{2}}\ {{t}_{3}}=({{v}_{1}}+{{v}_{2}}){{t}_{2}}\ \ \ \ \ \ \ (\because {{t}_{2}}={{t}_{3}})\] |
| \[\therefore \operatorname{Average} velocity=\frac{Total displacement }{Total time}\] |
| \[=\frac{s}{{{t}_{1}}+{{t}_{2}}+{{t}_{3}}}=\frac{s}{\frac{s}{2{{v}_{0}}}+\frac{s}{({{v}_{1}}+{{v}_{2}})}}\] |
| \[=\frac{2{{v}_{0}}({{v}_{1}}+{{v}_{2}})}{{{v}_{1}}+{{v}_{2}}+2{{v}_{0}}}\] |
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