One way to convert rotational motion into linear motion and vice versa is by the use of a mechanism called the Scotch yoke, which consists of a crank $C$ that is connected to a slider $B$ by a pin $A.$ The crank $C$ is mounted to a fixed bearing. The pin rotates with the crank while sliding within the yoke, which, in turn, rigidly translates with the slider. This mechanism has been used, for example, to control the opening and closing of valves in pipelines. Letting the radius of the crank be $R=25cm,$ determine the angular velocity vec$({)}_C$ and the angular acceleration vec$({)}_C$ of the crank at the instant shown if $=25$ and the slider is moving to the right with a constant speed $v_B=51\frac{m}{s}.($Round the final answers to four decimal places. Include a minus sign if nece ${?}^{-6}$ sary.$)$

The angular velocity of the crank is $$ hat$(k)ra\frac{d}{s}.$

The angular acceleration of the crank is $$ hat$(k)ra\frac{d}{s^2}$