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

 Problem 6. 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 [NEET 2011M]

(a) $\frac {v_1 v_2}{v_1 + v_2}$

(b) $\frac {2 v_1 v_2}{v_1 + v_2}$ 

(c) $\frac {2 v_1^2 v_2^2}{v_1^2 + v_2^2}$

(d) $\frac {v_1 + v_2}{2}$

\[Avg. Speed = \frac {Total \; distance}{Total \; time}\]

\[ = \frac {\frac{d}{2} + \frac {d}{2}}{\frac{d/2}{v_1}+\frac{d/2}{v_2}}\]

\[=\frac{2 v_1 v_2}{v_1+v_2}\]