Question

A person travels along a straight road for the first half time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then, the mean or average velocity $\overline{v}$ is given by

• A. $\overline{v}=\frac{v_1+v_2}{2}$
• B. $\frac{2}{\overline{v}}=\frac{1}{v_1}+\frac{1}{v_2}$
• C. $\overline{v}=\sqrt{v_1{v}_2}$
• D. $\overline{v}=\sqrt{\frac{v_2}{v_1}}$

Answer 1

The correct option is A $\overline{v}=\frac{v_1+v_2}{2}$

Let $t$ be the total time taken to cover the whole distance.
$\overrightarrow{v}=\frac{\text{Displacement}}{\text{time}}$
Displacement for first half = $v_1\frac{t}{2}$ Dispalcement for second hald = $v_2\frac{t}{2}$ $\Rightarrow \overline{v}=\frac{v_1\left(\frac{t}{2}\right)+v_2\left(\frac{t}{2}\right)}{t}=\frac{v_1+v_2}{2}$