1, 2, 3
Work Step by Step
We are given a graph of position and asked to rank the boxes according to their speed. 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 speed, greatest first, we have spring 1, then 2, then 3.