DYNAMICS $($MECHANICAL ENGINEERING$)$

Frame $B$ moves to the right from a rest position on the horizontal surface at a constant acceleration of $a_B=4\frac{m}{s^2}$ as shown in Figure Q$1.$ At the same time, collar $A$ is sliding down the shaft at a constant rate of $5\frac{m}{s}$ relative to frame $B.$

$($PLEASE REFER TO FIGURE GIVEN TO DRAW A FREE BODY DIAGRAM AND LABEL IT$)$

$($PLEASE GIVE ME THE FORMULA AND SHOW THE INSERTION VALUE ON YOUR SOLUTION $,$ AND GIVE THE ANSWER FOR EVERY QUESTION $)$THANKS$.$

a$)$ With the aids of diagrams, express the kinematic relationships between collar A and frame $B$ for velocity and acceleration.

$(3$ marks$)$

b$)$ Knowing that $=ta{n}^{-1}(\frac{3}{4}),$ determine the velocity and acceleration of collar A after frame $B$ has moved $2$ m $.$

$(5$ marks$)$

c$)$ Evaluate the kinematic of the collar if the frame moves at a constant velocity, $v_B$ on curved surface having a constant radius of curvature, $.$

$(2$ marks$)$