Question

Two particles of masses $2$kg and $4$kg are approaching towards each other with acceleration $1m/s^2$ and $2m/s^2$, respectively, on a smooth horizontal surface. Them find the acceleration of centre of mass of the system and direction of acceleration of $COM$.

Answer 1

The acceleration of $CM$ of the system is given by
$a_{CM}=\frac{m_1{a}_1+m_2{a}_2}{m_2+m_2}⟹a_{CM}=\frac{2\times 1+4(-2)}{2+4}=-1m/s^2$
Negative sign indicates that acceleration of $CM$ will be in the direction of acceleration of $4$kg mass.