Question

A person travelling in a straight line moves with a constant velocity v1 for certain distance 'x' and with a constant velocity $v_2$ for next equal distance. The average velocity v is given by the relation

• A. $\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}$
• B. $\frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}$
• C. $\frac{v}{2}=\frac{v_{1}+v_{2}}{2}$
• D. $v=\sqrt{v_{1}v_{2}}$

Answer 1

Answer: (B)

$\frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}$

Answer 2

Average velocity $= \frac{\text{Total distance}}{\text{Total time}}$ $= \frac{X + X}{ \frac{X}{V_1} + \frac{X}{V_2}}$ $\Rightarrow v = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}}$ $\Rightarrow \frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}$