A) \[\frac{{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\]
B) \[\frac{\text{2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\]
C) \[\frac{{{\text{v}}_{\text{0}}}\text{+.2}{{\text{v}}_{1}}+2{{\text{v}}_{2}}}{3}\]
D) \[\frac{{{\text{v}}_{\text{0}}}\text{+2(}{{\text{v}}_{1}}+{{\text{v}}_{2}})}{\text{(2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}})}\]
Correct Answer: D
Solution :
Let the total distance be d. Then for first half distance, time \[=\frac{\text{d}}{\text{2}{{\text{v}}_{\text{0}}}}\], next distance. = \[{{v}_{1}}t\]and last half distance = \[{{v}_{2}}t\] \[{{\text{v}}_{\text{1}}}\text{t+}{{\text{v}}_{\text{2}}}\text{t=}\frac{\text{d}}{\text{2}};\text{ t=}\frac{d}{2\left( {{v}_{1}}+{{v}_{2}} \right)}\] Now average speed \[t=\frac{d}{\frac{d}{2{{v}_{0}}}+\frac{d}{2\left( v{{ }_{1}}+{{v}_{2}} \right)}+\frac{d}{2\left( v{{ }_{1}}+{{v}_{2}} \right)}}\] =\[\frac{\text{2}{{\text{v}}_{\text{0}}}\left( \text{v}{{ }_{\text{1}}}\text{+}{{\text{v}}_{\text{2}}} \right)}{\left( \text{v}{{ }_{\text{1}}}\text{+}{{\text{v}}_{\text{2}}} \right)\text{+2}{{\text{v}}_{\text{0}}}}\]You need to login to perform this action.
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