Understanding Velocity
Explore the Rail Motion Demo first, if you have not already done so. Use the applet to the right to check your understanding of speed and velocity. Clicking "Go" will give you a new "target" graph of speed vs. time and a set of rails. Arrange the rails so that a ball will roll with the same speed at each time as the target graph. You can change the rail segments by clicking and dragging on the "hinges". By clicking "Check" you can see the motion, a motion diagram, and the actual speed of the ball (in red). You can repeatedly adjust the track to try for a better match.
This Illumination is not easy -- thought and practice are needed to do it efficiently. (Click on the ? button for suggestions.)