Physics - Center of Mass Question with Solution | TestHub

The acceleration of the center of mass of a system is given by $A_{CM}=\frac{F_{ext}}{M_{total}}$. Here, the external force is $F$ and the total mass of the system is $M_{total}=m_1+m_2$. So, the acceleration of the center of mass is $A_{CM}=\frac{F}{m_1+m_2}$. Since the system is initially at rest, the initial velocity of the center of mass is $V_{CM,0}=0$. For constant acceleration, the displacement of the center of mass is given by $S_{CM}=V_{CM,0}t+\frac{1}{2}{A}_{CM}{t}^2$.$$S_{CM}=(0)t+\frac{1}{2}\left(\frac{F}{m_1+m_2}\right)t^2=\frac{F{t}^2}{2(m_1+m_2)}$$