Critical Thinking Two boxes of the same mass are pressed against pistons that compress and release the boxes on frictionless surfaces. Box A's piston has a constant force F over a distance x before the box is released while box B starts at zero force and increases linearly to a force of 2F before releasing the box at a distance of 1/2 d.

(a) Which of these boxes has the greatest speed after releasing from the piston?

(b) Based on experimental data for trials similar to box A, an equation that fits the data is suggested for the change in kinetic energy, ΔKE, which may not be correct: ΔKE = KF^1/2 x^1/2, where K is a constant with appropriate units, F is the applied force, and x is the distance the piston moves in contact with the box. Is this equation consistent with your answer from part a? Explain why or why not. Does this equation make sense? Explain why or why not.

(c) If the applied force of the piston is proportional to the distance in contact with the box, graph the work done on the box vs. the distance in contact with the piston and box.