Answer
1, 3, 2
Work Step by Step
We are given a graph of position and asked to rank the boxes according to their maximum kinetic energy. Keep in mind that kinetic energy is a product of mass and the square of the velocity. The mass never changes, so therefore the greater the velocity of the box, the greater the kinetic energy will be. The derivative of position with respect to time is velocity so we can estimate the maximum velocity of each box by looking at the slope of the tangent line at the inflection points of each graph. Therefore the taller the graph is, the greater its maximum kinetic energy will be.
From the graph, we can see that the tallest graph is 1, followed by 3, and then 2.
