This Demonstration shows the connection between the graph of position versus time of motion with constant acceleration and the corresponding motion diagram. It helps to visualize and understand how the motion diagram depends on the initial conditions of position and velocity and the choice of acceleration.
Motion can be studied in a Cartesian coordinate system. Here we restrict the motion to be only in one dimension in the direction. (The and directions are independent of the direction and could be treated in the same way.)
The controls on the left change the character of the motion: you can choose the initial position , the initial velocity , and a constant acceleration . (The initial time is set to zero for convenience.) You can choose from one to five points that are spaced equally in time.
The controls on the right let you manipulate the points. You can change time between them, . You can project them to the axis to reduce the 2D plot to a 1D representation of the motion. Keep in mind that this simplification goes hand in hand with the condition that the time intervals between pairs of points are constant.
Finally, you can show the displacement vectors after the projection is done or switch the graph to the motion diagram.