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A child is sitting at one end of a long trolley moving with a uniform speed `v` on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed `u` (w.r.t. trolley), the speed of the centre of mass of the system will.

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The speed of the centre of mass of the system (trolley + child) shall remain unchanged, when the child gets up and runs about on the trolley in any manner. This is because forces involed in the exercise are purely internal i.e. from within the system. No external force acts on the system and hence there is no change in velocity of mass of the system.
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