Acceleration in space ?

Say a Spaceship of 1000 kg is at rest in space and suddenly produces thrust to accelerate it to 10 Km for 1 sec,now i know it continually moves at this speed from then on but what happens when the same amount of thrust is applied again to it, does it keep gaining 10 Km/s every second the thrust is applied increasing it to 600 Km/s in a minute or does it cancel out and remain at 10Km/s owing to the increase in m or does it increase fractionally ? Can someone tell the speed after a minute and the rate at which it will increase ?