A person travels x distance with velocity $\mathrm{v}_{1}$ and then x distance with velocity $\mathrm{v}_{2}$ in the same direction. The average velocity of the person is v , then the relation between $\mathrm{v}, \mathrm{v}_{1}$ and $\mathrm{v}_{2}$ will be :

(C) $\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$

(B) $v=\frac{v_{1}+v_{2}}{2}$

(D) $\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Kinematics

A person travels x distance with velocity

v_{1}

and then x distance with velocity

v_{2}

in the same direction. The average velocity of the person is v , then the relation between

v, v_{1}

and

v_{2}

will be :

Answer: (C)

Average velocity is total distance divided by total time. The person travels distance

x

v_{1}

(time

t_{1} = x / v_{1}

) and distance

x

v_{2}

(time

t_{2} = x / v_{2}

). Total distance is

2 x

and total time is

t_{1} + t_{2} = x / v_{1} + x / v_{2}

. Therefore, average velocity

v = \frac{2 x}{x / v _{1} + x / v _{2}} = \frac{2}{1/ v _{1} + 1/ v _{2}}

, which gives

\frac{2}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option