1, 2, 3 (zero)
Work Step by Step
We are given a graph of position and asked to rank the boxes according to their 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 velocity of each box by looking at the slope of the tangent line on the graph at $t=0$. From the graph, we can see that the slope of the tangent line on curve 1 is positive and steep, on curve 2 it is negative and shallow, and on curve 3 the slope is zero. Ranking them according to kinetic energy, greatest first, we have spring 1, then 2, then 3 (zero).