Incorrect takeoff data input to FMS. Prior to the departure of a Thomas Cook Airlines Airbus A330-200 from Montego Bay Jamaica during the hours of darkness on 28 October 2008, incorrect takeoff speeds had been input to the FMS by the flight crew without this being recognised and when rotation during take off was, as a consequence, initiated too early, the aircraft failed to become airborne as expected. The aircraft commander acting as PF quickly selected TOGA power and the aircraft became airborne before the end of the available runway had been reached and climbed away safely.