a
(a)For first condition Initial velocity \(= u\), Final velocity \(= u/2, s = 3 \,cm \) From \({v^2} = {u^2} - 2as\)

==> \({\left( {\frac{u}{2}} \right)^2} = {u^2} - 2as\)

==> \(a = \frac{{3{u^2}}}{{8s}}\)

Second condition Initial velocity\( = u/2\), Final velocity \(= 0\) From \({v^2} = {u^2} - 2ax\)

==>\(0 = \frac{{{u^2}}}{4} - 2ax\)  

\(x = \frac{{{u^2}}}{{4 \times 2a}} = \frac{{{u^2} \times 8s}}{{4 \times 2 \times 3{u^2}}} = s/3 = 1\,cm\)