Explanation

(a) If $u$ is the initial velocity then distance covered by it in $2\ sec$
$S = ut + \frac{1}{2}at^{2} = u \times 2 + \frac{1}{2} \times 10 \times 4 = 2u + 20\ \ \ \ \ \ \ \ldots(i)$
Now distance covered by it in 3$^{rd}$ $\sec$
$S_{3^{rd}} = u + \frac{1}{2}(2 \times 3 - 1)10 = u + 25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
From (i) and (ii), $2u + 20 = u + 25 \Rightarrow u = 5$
$\therefore S = 2 \times 5 + 20 = 30\ m$