A child sits stationary at one end of long trolley moving uniformly with speed v on a smooth horizontal floor. If the child gets up and runs about on the trolley in the forward direction with speed u. The centre of mass of the system (child + trolley) will move with speed
v
The speed of the centre of mass of the system remain unchanged (equal to v) because no external force acts on the system. The force involved such as action and reaction, friction etc when the child runs on the trolley are internal to the (trolley+child) system.