Linked Position, Velocity, and Acceleration Graphs via a Velocity-Time Editor

This example lets you reshape a Velocity vs. Time graph by sliding its control points up or down, while simultaneously visualizing the corresponding Position vs. Time and Acceleration vs. Time graphs. It highlights how the “shape” of one kinematics graph determines the other two, offering an intuitive bridge between graph transformations and calculus-style rates of change. Key concepts include function graphs, the slope interpretation (velocity as the time-rate of change of position) and acceleration as the time-rate of change of velocity. Construction-wise, the GeoGebra setup relies on geometric primitives from the provided summary: Segment to build the required line/graph pieces, Point to define control and sampling points, and Midpoint to compute reference midpoints that support consistent segment relationships and correspondences across time intervals. Objects such as A, B, C, D and their indexed counterparts (e.g., A_1, B_1, C_1…; A_2, B_2, C_2…) represent different time nodes or piecewise components used to assemble the linked graphs. Suitable for late secondary school through early university, especially for motion-graph interpretation and teaching intuition for derivatives/rates.