Since the two particles initially at rest move toward each other under their mutual force of attraction, no external force acts on the system. According to the conservation of linear momentum, if the net external force acting on a system is zero, its total linear momentum remains constant, which implies the acceleration of the centre of mass is zero. Therefore, the velocity of the centre of mass remains constant. Since both particles were initially at rest, the initial velocity of the centre of mass was zero. Thus, the speed of the centre of mass at any instance will remain zero, regardless of the individual speeds of the particles.