The equation $M\vec{A} = \vec{F}_{ext}$ denotes what?

The velocity of the centre of mass of the system as shown in the figure is

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

Obtain an expression for the velocity of the centre of mass for a system of $n$ particles.

$A$ mass $m$ is at rest on an inclined plane of mass $M$,which is further resting on a smooth horizontal plane. Now,if the mass $m$ starts moving under gravity,the position of the centre of mass of the system will

$A$ cart of mass $M$ is tied to one end of a massless rope of length $10\, m$. The other end of the rope is held by a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $x = 0$ and the cart is at $x = 10\, m$. If the man pulls the cart by the rope,the man and the cart will meet at the point: