Explanation

(a) For first condition
Initial velocity = $u$, final velocity $= u/2,\ s = 3\ cm$
From $v^{2} = u^{2} - 2as \Rightarrow \left( \frac{u}{2} \right)^{2} = u^{2} - 2as \Rightarrow a = \frac{3u^{2}}{8s}$
Second condition
Initial velocity $= u/2$, Final velocity $= 0$
From $v^{2} = u^{2} - 2ax \Rightarrow 0 = \frac{u^{2}}{4} - 2ax$
$\therefore x = \frac{u^{2}}{4 \times 2a} = \frac{u^{2} \times 8s}{4 \times 2 \times 3u^{2}} = s/3 = 1cm$