In a mechanism $($Fig$.$P$1\mathrm{.}30),$ a plate is connected to two identical telescopic arms, which are given identical rotations. A pin moves relative to a smooth slot, with its centre $P$ following the path $x=0\mathrm{.}9-2y^2+y^3,$ where $x,y$ are in metres. At the instant shown, the lengths of both the arms are increasing at $0\mathrm{.}8\frac{m}{s}$ and this rate itself is decreasing at the rate of $0\mathrm{.}2\frac{m}{s^2}.$ The location of $P$ at this instant is at $y=0\mathrm{.}3m$ and its speed is $v=2\frac{m}{s}$ increasing at an unknown rate $v^{}$ relative to the plate. Find vec$(a{)}_D$ and $v^{}.$