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A body covers half the distance with a speed of $20 m / s$ and the other half with a speed of $30 m / s$ . The average velocity of the body during the whole journey is__?

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Zero

24 m / s

25 m / s

None of these

answer is B.

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Detailed Solution

The average velocity of the body during the whole journey is

24 m / s

.
Let the total distance be

2 x

.
For first half distance

Speed = 20 m / s

Thus, time taken

t_{1} = \frac{x}{20}

For second half distance:

Speed = 30 m / s

Thus, time taken

t_{2} = \frac{x}{30}

Average velocity,

V_{avg} = \frac{2 x}{t_{1} + t_{2}}

\Rightarrow V_{avg} = \frac{2 x}{\frac{x}{20} + \frac{x}{30}}

⇒

V_{avg} = \frac{2 \times 20 \times 30}{20 + 30}

⇒

V_{avg} = 24 m / s

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