8. A person travelling in a straight line moves with a constant velocity v1 for certain distance ’ x ’ and with a constant velocity v2 for next equal distance. The average velocity v is given by the relation

8. A person travelling in a straight line moves with a constant velocity v1 for certain distance ’ x ’ and with a constant velocity v2 for next equal distance. The average velocity v is given by the relation

(a) v = \( \sqrt{v_1 v_2} \)

(b) \( \dfrac{1}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2} \)

(c) \( \dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2} \)

(d) \( \dfrac{v}{2} = \dfrac{v_1 + v_2}{2} \)

Answer :  (c) \( \dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2} \)

\( \text{Average Velocity} = \dfrac{\text{total distance}}{\text{total time}} \)

\( = \dfrac{x + x}{\dfrac{x}{v_1} + \dfrac{x}{v_2}} \)

\( = \dfrac{2x}{x\left(\dfrac{1}{v_1} + \dfrac{1}{v_2}\right)} \)

\( \text{Therefore  v}= \dfrac{2}{\dfrac{1}{v_1} + \dfrac{1}{v_2}} \)

\(  \rightarrow  \dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2} \)