In this paper, we present a problem of regulating the motion of a rolling ball in a one-dimensional space in the presence of non-linear effects of friction and contact. The regulation problem is solved using a model-based reinforcement learning technique. A Gaussian process model is learned to make predictions on the motion of the ball and then, the predictive model is used to solve for the control policy using dynamic programming by estimating the value functions. Several results are shown to demonstrate the simple, yet interesting motion dynamics for the ball. Our hope is that the proposed system will serve as a simple benchmark system for reinforcement and robot learning.