Rack $A$ on the left is moving downward. The rack causes the two gears to rotate, which in turn causes the right rack $B$ to translate. Left gear $C$ rotates from rest with an angular acceleration of $1\mathrm{.}2ra\frac{d}{s^2}$ counter$-$clockwise. $r_1=0\mathrm{.}15m$ and $r_2=0\mathrm{.}1m.$

After the geachas turned $2$ revolutions, determine:

$($a$)$ the velocity of rack $B$;

$($b$)$ the velocity of Point $D$;

$($c$)$ the normal acceleration, the tangential acceleration, and the total acceleration at Point D $.$