QJEEM23Ph9df1: JEE Main 2023 Physics - Class 11 JEEM23Ph9df1 Solution: A person travels distance with velocity and then distance with…

The average velocity is defined as the total displacement divided by the total time. Here, the person travels the same distance $x$ twice, once with velocity $v_1$ and once with velocity $v_2$ .

The time to travel distance $x$ with velocity $v_1$ is $t_1 = \frac{x}{v_1}$ , and the time to travel distance $x$ with velocity $v_2$ is $t_2 = \frac{x}{v_2}$ .

The total time is then

$t = t_1 + t_2 = \frac{x}{v_1} + \frac{x}{v_2}$ .

The total displacement is $2x$ . So, the average velocity $v$ is given by

$v = \frac{\text{total displacement}}{\text{total time}} = \frac{2x}{\frac{x}{v_1} + \frac{x}{v_2}} = \frac{2}{\frac{1}{v_1} + \frac{1}{v_2}}$

Multiplying both sides by $2$ , we get

$\frac{2}{v} = \frac{1}{v_1} + \frac{1}{v_2}$