(a) The net force on the system (of total mass $$M = 80.0\, kg$$ is the force of gravity acting on the total overhanging mass $$(m_{BC} = 50.0 kg)$$. The magnitude of the acceleration is therefore $$a = (m_{BC}\, g)/M = 6.125\, m/s^2$$. Next we apply Newton’s second law to block C itself (choosing down as the +y direction) and obtain
$$m_Cg - T_{BC} = m_Ca$$.
This leads to $$T_{BC} = 36.8\, N$$.
(b) We use Eq. 2-15 (choosing rightward as the +x direction): $$\Delta x = 0+\frac {1}{2}at^2= 0.191 \, m$$