Block B starts from rest. Block A moves with a constant acceleration and slider. Block C moves to the right with a constant acceleration of $83m\frac{m}{s^2}.$ At $t=3$ seconds, the velocitles of $B$ and $C$ are $500m\frac{m}{s}$ downward and $300m\frac{m}{s}$ to the right. Determine

a$)$ The acceleration of Block A $($provide magnitude and direction$)$

b$)$ The acceleration of Block B $($provide magnitude and direction$)$

c$)$ The initial velocity of Block A $($provide magnitude and direction$)$

d$)$ The initial velocity of Block B $($provide magnitude and direction$)$

e$)$ The change in position of slider Block $C$ after $3$ seconds $($provide magnitude and direction$)$