c
\(a=\frac{- kx }{2}=\frac{-12 x }{2}=-6 x\)

\(\frac{ v d v }{ dx }=-6 x\)

\(\int \limits_{4}^{*} vdv =-\int \limits_{\frac{1}{2}}^{ s / 2} 6 xdx\)

\(\frac{ v ^{2}-4^{2}}{2}=-\frac{6}{2}\left[\left(\frac{3}{2}\right)^{2}-\left(\frac{1}{2}\right)^{2}\right]\)

\(v ^{2}-16=-6\left(\frac{9}{4}-\frac{1}{4}\right)\)

\(v ^{2}=16-6 \times 2=4\)

\(V =2\,m / s\)