• # question_answer A particle covers half of its total distance with speed ${{v}_{1}}$and the rest half distance with speed ${{v}_{2}}.$Its average speed during the complete journey is A) $\frac{{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}$B) $\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}$C) $\frac{2v_{1}^{2}v_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}$D) $\frac{{{v}_{1}}+{{v}_{2}}}{2}$

Velocity $v=\frac{s}{y}\Rightarrow s=vt$ The average speed of particle ${{v}_{av}}=\frac{s+s}{\frac{s}{{{v}_{1}}}+\frac{s}{{{v}_{2}}}}$ $\Rightarrow$ ${{v}_{av}}=\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}$