$(30$ Points, manually graded, show all work clearly$)$

One rope is attached to the right$-$side wall, goes around Pulley D$,$ and is being

wound up by the motor at a rate of $v_m(t)13*t_{\text{i}\text{m}\text{e}}^{2}f\frac{t}{s}($where time is in

seconds$).$ A second rope is attached to the left$-$side wall, goes around Pulleys

$B$ and $C,$ then terminates at the axis of Pulley D$.$

a$)$ Find the acceleration of Pulley D as a function of time, indicating direction.

b$)$ Find the acceleration of Block$/$Pulley $B$ at $t_{\text{f}\text{i}\text{n}\text{a}\text{l}}=9s,$ including direction.

Note: To receive full credit, you must use the datum method shown in class

and must interpret the numerical results accordingly.

You might find it helpful to use a different datum for Part a$)$ than for Part b$).$

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