If a man starts running on a boat with an acceleration $a$ with respect to the boat, there is no external force that acts on the Boat+Man system (assuming friction due to water to be zero and neglecting air drag). But the velocity of system increases. What causes the increase in kinetic energy even if there is no external force?
I have not neglected friction between man and boat. But in boat+man system, its not an external force. Gravity does not do any work since displacement of boat is perpendicular to force due to gravity.