(Solved): For the shown pulley system, if the block C has a mass mC =3.5(x)kg is moving to the downward wi ...

For the shown pulley system, if the block $C$ has a mass $m_C$ $=3.5(x)\mathrm{kg}$ is moving to the downward with a velocity $v_D(t)$ $=\left(\frac{y}{40}{t}^{2.5}?\frac{x}{8}t+3\right)\mathrm{m}/\mathrm{s}$, and the block $\mathrm{D}$ has a mass $m_D$ $=8(y)\mathrm{kg}$ is moving to the upward at constant acceleration of $a_C=\left(\frac{x+y}{5}\right)\mathrm{m}/{\mathrm{s}}^2$, as shown. If the system motion started from rest, calculate (i) the distance moved by block $\mathrm{C}$ at $t=3\mathrm{s}$. (ii) the magnitude and direction of displacement for the cylinder $\mathrm{G}$ at $t=5\mathrm{s}$. (iii) the magnitude and direction of acceleration of cylinder $\mathrm{G}$ at $t=5\mathrm{s}$, (iv) the magnitude and direction of velocity of cylinder $\mathrm{G}$ at $t=5\mathrm{s}$.