Q$3$

Two forces $(4i-2j)N$ and $(2i+qj)N$ act on a particle $P$ of mass $1\mathrm{.}5kg.$ The resultant of these two forces is parallel to the vector $(2i+j).$

$($a$)$ Find the value of $q.$

At time $t=0,P$ is moving with velocity $(-2i+4j)m{s}^{-1}.$

$($b$)$ Find the speed of $P$ at time $t=2$ seconds.