Centre of mass moves with constant velocity The centre of mass of the Newton $n$-body problem is given by $$S=\frac{1}{M} \sum m_ix_i$$ with $M=\sum m_i$.
Show that it moves with contant speed and hence has no acceleration.
I don't understand as if I differentiate, I'll surely just get $$S'=\frac{1}{M} \sum m_ix'_i$$ which is not constant...is it?

This system is closed, that is $\sum\overrightarrow{F}=\vec{0}=\sum m_i\ddot{x}_i=M\ddot{S}$ which implies $\dot{S}=constant$
