6. A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is

6. A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. 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) \( \frac{2 v_1^2 v_2^2}{v_1^2 + v_2^2} \)

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

Answer : (b) \( \frac{2 v_1 v_2}{v_1 + v_2} \)

\( \text{Average speed} = \)\(\frac{\text{Total distance}}{\text{Total time}} \)

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

\( = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}} \)

\( = \frac{2 v_1 v_2}{v_1 + v_2} \)