$2.\backslash ($ A $\backslash )$ car engine with piston geometry illustrated in Figure $\backslash ($ Q $2\backslash )$ has its crank $\backslash ($ A B $\backslash )$ rotating about $\backslash ($ A $\backslash )$ with constant anticlockwise angular velocity $1000$ rpm $.$ The crank length $\backslash ($ A B $\backslash )$ is $7$ cm $,$ the connecting rod length $\backslash ($ B C $\backslash )$ is $14$ cm and the piston is constrained to move vertically. At the position shown:

$($a$)$ Draw a simplified sketch of the velocities relating to the crank, connecting rod and piston.

$($b$)$ What angular velocity does the connecting rod have $($in rad$/$s$)?$

$\backslash (46\mathrm{.}83\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$

$($c$)$ Draw a simplified sketch of the accelerations relating to the same three components.

$($d$)$ What angular acceleration does the connecting rod have $($in $\backslash (\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ))?$

$[5$ marks$]$