A vehicle travels 4 km with speed of $3 \mathrm{~km} / \mathrm{h}$ and another 4 km with speed of $5 \mathrm{~km} / \mathrm{h}$, then its average speed is :

(D) $3.75 \mathrm{~km} / \mathrm{h}$

(A) $4.25 \mathrm{~km} / \mathrm{h}$

(B) $3.50 \mathrm{~km} / \mathrm{h}$

(C) $4.00 \mathrm{~km} / \mathrm{h}$

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Kinematics

A vehicle travels 4 km with speed of

3 km / h

and another 4 km with speed of

5 km / h

, then its average speed is :

(A) $4.25 km / h$
(B) $3.50 km / h$
(C) $4.00 km / h$
(D) $3.75 km / h$ ✓ Correct

Answer: (D)

Solution

Equal distances of

4

km are covered at the two speeds, so the average speed is the total distance divided by the total time,

v_{av} = \frac{4 + 4}{\frac{4}{3} + \frac{4}{5}}

. The total time is

4 (\frac{1}{3} + \frac{1}{5}) = 4 \times \frac{8}{15} = \frac{32}{15}

h, so

v_{av} = \frac{8 \times 15}{32} = 3.75

km h

^{- 1}

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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