Explanation

(c) When a particle is moving with uniform acceleration, let $v$ be the velocity of particle at a distance $s$,
Then average velocity $= \frac{0 + v}{2} = \frac{v}{2}$
Time taken, $t_{1} = \frac{s}{(v/2)} = \frac{2s}{v}$
When particle moves with uniform velocity, time taken, $t_{2} = \frac{2s}{v}$
When particle moves with uniform acceleration,
Time taken, $t_{3} = \frac{3s}{(0 + v)/2} = \frac{6s}{v}$
Total time$= t_{1} + t_{2} + t_{3} = \frac{2s}{v} + \frac{2s}{v} + \frac{6s}{v} = \frac{10s}{v}$
$\therefore\ v_{av} = \frac{s + 2s + 3s}{10s/v} = \frac{6v}{10}$ or $\frac{v_{av}}{v} = \frac{6}{10} = \frac{3}{5}$