A body covers the first half of the distance with a velocity v and the second half in double the time taken for the first half. The average velocity is

$v$

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$\frac{v}{2}$

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$\frac{2 v}{3}$

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$\frac{2}{3 v}$

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Solution

The correct option is C
$\frac{2 v}{3}$

Step 1:Given data and assuptions:
Velocity for the first half of the distance = v
Body covers the second half in double the time taken for the first half.
Let the distance for the whole journey be = 2d
Step 2:Finding the average velocity:
Time taken for the first half of the journey = $\frac{d}{v}$
Time taken for the second half of the journey = $\frac{2 d}{v}$
Total time for the whole journey = $\frac{d}{v} + \frac{2 d}{v} = \frac{3 d}{v}$
Average velocity = $\frac{T o t a l d i s p l a c e m e n t}{T o t a l t i m e t a k e n}$
Average velocity = $\frac{2 d}{\frac{3 d}{v}} = \frac{2 v}{3}$
Thus, the average velocity is $\frac{2 v}{3}$ .
Hence, option C is correct.

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