A $2\mathrm{.}3$ kg block is connected by a rope across a $30$ cm diameter, $5\mathrm{.}0$ kg $,$ frictionless pulley as shown. A constant $14$ N force is applied to the other end of the rope. The moment of inertia of the pulley is $I=\frac{1}{2}M{R}^2.$ Use $g=9\mathrm{.}8\frac{m}{s^2}.[$Answer in $2$ significant figures$]$

a$)$ Draw the free body diagram for the block. Include coordinate axis and direction of the acceleration in the diagram.

b$)$ Draw the rigid body diagram for the pulley. Include the direction of angular acceleration of the pulley.

c$)$ Find the tension $T$ of the rope.

d$)$ Starting from rest, how long does it take the block to move $20$ cm $?$