Final answer:
If the friction force opposing a push on a box is of the same magnitude, there is no net force and thus no acceleration. The box will not change its state of motion unless an unbalanced force is applied. Newton's laws of motion are critical to understanding these dynamics.
Step-by-step explanation:
If you are pushing a large box across the carpet and the opposing friction force has the same magnitude as your push, the direction of the acceleration of the box is zero. This is because the net external force acting on the box is zero, and according to Newton's first law of motion, an object with no net external force acting on it will maintain its state of motion. In this case, if the box was initially at rest, it would stay at rest, and if it was moving at a constant velocity, it would continue to move at that velocity. The forces cancel each other out entirely, and thus, there is no acceleration.
However, if we take a different example where a person is pushing a lawn mower and the force exerted is greater than the friction, then the mower would accelerate in the direction of the person's push, which is parallel to the ground. This situation differs from the large box example because here, the forces do not cancel out, which results in a net external force that causes acceleration of the mower.
Newton's first and second laws are fundamental when determining the net force and resulting acceleration of objects. The first law, also known as the law of inertia, indicates that an object will not change its velocity without an unbalanced force. The second law, F=ma, relates the net force acting upon an object to its mass and acceleration, further explaining that the direction of the acceleration is the same as the direction of the net force.