The center-of-mass motion is determined by the net external force, even when the particles are not interacting. Practice with center-of-mass coordinates.
Consider two particles of equal mass \(m\). The forces on the particles are \(\vec F_1=0\) and \(\vec F_2=F_0\hat{x}\) (for this problem, ignore gravitational forces between the two particles). If the particles are initially at rest at the origin, find the position, velocity, and acceleration of the center of mass as functions of time. Solve this problem in two ways,