Two particles of masses $$2$$kg and $$4$$kg are approaching towards each other with acceleration $$1 m/s^2$$ and $$2 m/s^2$$, respectively, on a smooth horizontal surface. Them find the acceleration of centre of mass of the system and direction of acceleration of $$COM$$. The acceleration of $$CM$$ of the system is given by$$a_{CM} = \dfrac{m_1a_1 + m_2a_2}{m_2+ m_2} \Longrightarrow a_{CM} = \dfrac{2 \times 1 + 4 (-2)}{ 2 + 4} = -1 m/s^2$$
Negative sign indicates that acceleration of $$CM$$ will be in the direction of acceleration of $$4$$kg mass.