Question

A person completes half of his journey with speed $v_1$ and rest half with speed $v_2$. The average speed ($v_{avg})$ of the person is

• A. $\frac{v_1+v_2}{2}$
• B. $\frac{2v_1{v}_2}{v_1+v_2}$
• C. $\frac{v_1{v}_2}{v_1+v_2}$
• D. $\sqrt{v_1{v}_2}$

Answer 1

The correct option is B $\frac{2v_1{v}_2}{v_1+v_2}$

In this problem total distance is divided into two equal parts.

Let the total distance be d
So$v_{avg}=\frac{d_1+d_2}{\frac{d_1}{v_1}+\frac{d_2}{v_2}}=\frac{\frac{d}{2}+\frac{d}{2}}{\frac{d/2}{v_1}+\frac{d/2}{v_2}}\Rightarrow v_{av}=\frac{2}{\frac{1}{v_1}+\frac{1}{v_2}}=\frac{2v_1{v}_2}{v_1+v_2}$