(D)
$\vec{F}=(-3 \hat{i}+4 \hat{j})$
$m \vec{a}=(-3 \hat{i}+4 \hat{j})$
$M=5 \mathrm{~kg}$
$\vec{a}=\left(\frac{-3}{5} \hat{i}+\frac{4}{5} \hat{j}\right) \Rightarrow \vec{a}=a_{x} \hat{i}+a_{y} \hat{j}$
$a_{x}=\frac{-3}{5}$
at $\mathrm{t}=0$
$\vec{V}_{0}=(6 \hat{i}-12 \hat{j}) \Rightarrow\left(V_{o x} \hat{i}-V_{o y} \hat{j}\right)$
$V_{o x}=6$
For the body to have velocity along y-axis only, x-component of velocity should be zero i.e., $V_{x}=0$
$V_{x}=V_{o x}+a_{x} t$
$0=6+\left(\frac{-3}{5}\right) t$
$6=\frac{3}{5} t$
$t=\frac{6 \times 5}{3}=10 s$
OR
$A=\frac{F}{m}=\left(-\frac{3}{5} \hat{i}+\frac{4}{5} \hat{j}\right)$
$\mathrm{u}=(6 \hat{i}-12 \hat{j}) \mathrm{m} s^{-1}$
$\mathrm{v}=\mathrm{u}+$ at.
$1 \hat{j}=(6 \hat{i}-12 \hat{j})+\left(-\frac{3}{5} \hat{i}+\frac{4}{5} \hat{j}\right) t$