A student pushes a heavy box across a rough horizontal floor at a constant velocity. The student then increases the pushing force. Explain what happens to the motion of the box after the pushing force is increased, and explain why.

At constant velocity the student’s pushing force is balanced by the kinetic friction force, so the net force is zero.

If the student increases the pushing force, the net force on the box becomes positive (in the direction of the push). Consequently the box accelerates and its speed increases.

As the speed rises, the kinetic friction force (which is proportional to the normal force and independent of speed) remains the same, but the net force decreases as the box accelerates. The friction force does not increase with speed; however, the increased speed eventually leads to a new balance when the pushing force equals the kinetic friction force again.

At that point the net force is zero once more and the box moves at a new, higher constant velocity (its terminal velocity).