Problem $3(10$ points$)$: Cylinder $B$ has a downward velocity in feet per second given by

$v_B=\frac{t^2}{2}+\frac{t^3}{6},$ where $t$ is in seconds. Show that, when $t=2sec,$ the acceleration of $A$ is

$2f\frac{t}{se{c}^2}$ upward.