3.1: Particle kinematics with column vectors

Find the velocity vector of $A$.

Given that $A$ is initially at the point with position vector $\begin{pmatrix} 5 \\ -3 \end{pmatrix}$, write down the position vector of $A$ at time $t$.

A particle $B$ starts to move such that its position vector at time $t$ is $\begin{pmatrix} -35t + 4 \\ 44t - 2 \end{pmatrix}$.

Find the displacement vector $\overrightarrow{AB}$ at time $t$.

Hence find the distance $AB$, at time $t$, in the form $\sqrt{pt^{2} + qt + r}$, where $p$, $q$ and $r$ are constants.

Find the value of $t$ when the distance $AB$ is $6$, giving your answer correct to $2$ decimal places.