Final answer:
The leftmost box will move with constant velocity while the rightmost box accelerates.
Step-by-step explanation:
The correct statement about what will happen to the boxes is c. the leftmost will move with constant velocity while the rightmost box accelerates. The leftmost box will move with constant velocity while the rightmost box accelerates.
When a constant force is exerted on the leftmost box, it will experience an equal and opposite force from the rightmost box due to the string connecting them.
Therefore, the leftmost box will move with constant velocity. However, the rightmost box will accelerate because the net force acting on it is not zero.