Final answer:
A horizontal force applied directly through a box's center of gravity on a smooth floor will cause the box to move with constant acceleration in the direction of the force, without rotation, according to Newton's first law of motion.
Step-by-step explanation:
When a horizontal force is applied to a box through its center of gravity, and the box is resting on a smooth (frictionless) surface, several physics principles come into play. Specifically, we rely on Newton's first law of motion, which states that an object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an unbalanced force. In this scenario, the horizontal force acts on the center of gravity, which means there won't be any rotational motion, and the box will begin to move in the direction of the force with a constant acceleration.
If we were to consider a situation where friction is not negligible, then we must look at Newton's second law of motion and factor in the frictional force. The static coefficient of friction between the box and the floor would determine the maximum force that can be applied without moving the box. If the applied horizontal force is greater than the frictional force, the box will start to move.