Answer: continue with constant velocity.
Newton's first law states that motion requires no force.
After the cart is released, there is no longer a force in the x-direction. The cart will continue continue moving with the same velocity it had at the moment of release.
The initial push got the cart moving, but that force is not needed to keep the cart in motion.
This is because of Newton's first law which states that an object in motion continues to move at constant velocity in the absence of external forces.