Acceleration x vs Time t

xo(m)   vo (m/s)   ao(m/s2)   da/dt(m/s3)
A straight horizontal line in an acceleration versus time graph means that the acceleration is constant. This obviously means that the velocity is changing at a constant rate and that the position is changing at a changing rate.
An acceleration versus time graph provides no information on the initial velocity or initial position of the puck. They are here arbitrarily selected to be zero.
Don't forget that the initial position and the initial velocity of the puck in the simulation were chosen arbitrarily.