The following is the law of conservation of momentum (in terms of velocity):
$$m_1\mathbf{v_1} + m_2 \mathbf{v_2} = m_1 \mathbf{v_1}^\prime + m_2 \mathbf{v_2}^\prime.$$
Does the law of conservation of momentum also hold for position and acceleration? Since position and acceleration are the $0$th and $2nd$ derivatives (of position), respectively, I suspect that it does. If so, then, putting the law of conservation in terms of position, we get
$$m_1 \mathbf{r_1} + m_2 \mathbf{r_2} = m_1 \mathbf{r_1}^\prime + m_2 \mathbf{r_2}^\prime.$$
I would greatly appreciate it if someone would please take the time to clarify this.