A student pushes a heavy box that is already moving across a rough floor. If the force applied by the student is exactly equal to the frictional force opposing the motion, what will happen to the box?
The box will move at a constant speed
This problem is answered using Newton's First Law of Motion (the law of inertia), which states that a body continues in its state of rest or of uniform motion in a straight line unless acted upon by a net (unbalanced) external force. The key is that motion at constant velocity requires zero net force — an object does not need a surplus of force to keep moving, only to change its motion.
Here the box is already moving across a rough floor. The student pushes it forward, and friction acts backward opposing the motion. Because the applied force is stated to be exactly equal to the frictional force, the two cancel:
Net force = Applied force − Friction = 0
With zero net force there is zero acceleration, so the velocity does not change. Since the box was already in motion, it continues to move at a constant speed — the correct answer.
The other options misread the balance of forces:
- The box would only accelerate forward or move at increasing speed if the applied force exceeded friction, giving a net forward force — but here the forces are balanced.
- The box would gradually come to rest only if friction exceeded the applied force, giving a net backward force that slows it down — again not the case when the two are equal.
So a balanced pair of forces on an already-moving object produces steady, unchanging motion, not acceleration or stopping.
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