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 is a direct application of Newton's First Law of Motion (the law of inertia): 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 phrase in the question is that the box is already moving, so we only need to check whether the forces on it are balanced.
The horizontal forces are the student's applied force (forward) and kinetic friction (backward). Since the problem states these are exactly equal:
Net Force = Applied Force − Friction = 0
By Newton's Second Law, Fnet = ma, so if Fnet = 0 then acceleration a = 0. Zero acceleration on an object that is already in motion means its velocity does not change — the box moves at a constant speed. This is the correct answer.
The other options each require a non-zero net force, which does not exist here. The box would accelerate forward or move at increasing speed only if the applied force exceeded friction, and it would gradually come to rest only if friction exceeded the applied force. With the two forces balanced, none of these happens; the motion simply continues unchanged.
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