Q$3.[$Total $6$ marks$]$ A circular disk of radius $200$ mm rolls to the left without slipping, as shown below:

For the instant shown, the acceleration of point $A$ on the edge of the disk relative to point $O$ at the center of disk is $a_{\frac{A}{O}}=2i-5j\frac{m}{s^2},$

a$)[2$ marks$]$ Draw the vector polygon for the acceleration of points A and $O.$

b$)[4$ marks$]$ determine the velocity and acceleration of the center of the disk $O.$