Position vs Time, Velocity vs Time, and Acceleration vs Time Graphs Review

When an object is rolling down a ramp, the graphs of this action should look like the following:

 

(replace the word displacement with position), image via http://www.thefullwiki.org/FHSST_Physics/Rectilinear_Motion/Graphs

As you can see, the position gradually increases more and more per second, meaning the velocity increases constantly and the object is constantly acceleration.  We also discovered in class that the slope of the position is the velocity and that the slope of the velocity is the acceleration, which explains why the graphs go from being a curve to linear to a straight line.

This means when the position increases at a constant rate, the velocity has a slope of zero (straight line across) and there is no acceleration, as shown below: 

image via http://www.bbc.co.uk/bitesize/higher/physics/mech_matt/analyse_motion/revision/1/