A student constructs three separate graphs—position vs. time, velocity vs. time, and acceleration vs. time—to describe the motion of a low-friction cart during a 6s experiment.
1. Position graph: From t=0s to t=3s the curve is concave upward, starting at x=0m and reaching x=9m. From t=3s to t=6s the graph is a straight line with slope +2m/s, ending at x=15m.
2. Velocity graph: From t=0s to t=3s the line rises uniformly from 0m/s to 6m/s. From t=3s to t=6s the velocity remains constant at 6m/s.
3. Acceleration graph: From t=0s to t=3s the acceleration is a constant +2m/s2. From t=3s to t=6s the acceleration is 0m/s2.
All three graphs have identical, aligned time axes.
(a) Identify which one of the three graphs is inconsistent with the other two.
(b) Provide two distinct quantitative arguments—one involving a slope comparison and one involving an area comparison—that demonstrate the inconsistency you identified in part (a).
(c) Sketch a corrected version of the inconsistent graph on appropriately labeled axes so that it now matches the other two graphs.
(d) Using your corrected set of graphs, determine the cart’s total displacement during the 6s interval.