Students have difficulty relating real world motions to a graph and vice-versa.

To probe this difficulty, construct a ball and track set-up in class (perhaps like the diagram below), and ask the students to plot the position and velocity of the ball versus time. Alternatively, you can give them a plot of a particle's postion or velocity versus time, and ask them to reproduce the motion on their desktops.

Velocity:

The ball initially speeds up down the incline. Along the flat section it will travel at a constant speed (frictionless surface). It will decrease speed up the ramp, change direction, and speed up down the incline (now headed in the opposite direction). If the original direction (to the right) is chosen to be the positive direction, when the ball travels is traveling to the left it must be travelling in the negative direction. This is shown on a velocity versus time graph by plotting the velocity below the v=0 axis (similar to plot below).

Position:

The ball is initially speeding up down the incline, so the slope of the position graph will be increasing as it moves to the right (chosen as the positive direction in the plot below). The slope becomes constant, but still positive, while the ball travels along the flat section of the track. Then the slope decreases as the ball climbs up the far ramp. The slope becomes zero and then negative as the ball reaches the turnaround point and begins to head back toward the starting position (chosen as x = 0 in the plot below).