A cart is released from rest at the top of a smooth inclined plane. A motion sensor tracks the cart's position \(x\) relative to its starting point as a function of time \(t\). A student wants to test the hypothesis that the cart moves with a constant acceleration \(a\). If the student plots the position \(x\) on the vertical axis, what should be plotted on the horizontal axis to produce a linear graph, and what does the slope of that line represent?