A car travels a distance of 'x' with speed $\mathrm{V}_{1}$ and then same distance 'x' with speed $\mathrm{V}_{2}$ in the same direction. The average speed of the car is:

(D) $\frac{2 v_{1} v_{2}}{v_{1}+v_{2}}$

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

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Kinematics

A car travels a distance of 'x' with speed

V_{1}

and then same distance 'x' with speed

V_{2}

in the same direction. The average speed of the car is:

(A) $\frac{v _{1} v _{2}}{2 ( v _{1} + v _{2} )}$
(B) $\frac{v _{1} + v _{2}}{2}$
(C) $\frac{2 x}{v _{1} + v _{2}}$
(D) $\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}$ ✓ Correct

Answer: (D)

Solution

Average speed is the total distance divided by the total time. For two equal stretches

x

at speeds

v_{1}

and

v_{2}

, the total distance is

2 x

and the total time is

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

. Hence

\overset{v}{ˉ} = \frac{2 x}{x ( \frac{1}{v _{1}} + \frac{1}{v _{2}} )} = \frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

, the harmonic mean of the two speeds.

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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