Understanding Acceleration
Explore the Rail Motion Demo first, if you have not already done so. Click "Go" and you get a new "target" graph of acceleration vs. time and a set of rails. Arrange the rails so that a ball will roll with the same acceleration as the target graph. Change the rail segments by clicking and dragging on the "hinges". Clicking "Check" will reveal the motion, a motion diagram, and the actual acceleration of the ball (in red). You can repeatedly adjust the track to try for a better match. The positive direction of the acceleration is taken to be parallel to each rail segment, in the direction of the ball's motion.
This Illumination is not easy -- thought and practice are needed to do it efficiently. (Click on the ? button for suggestions.)