A cart of mass \(m\) accelerates from rest along a straight, horizontal track. The cart's electric motor delivers a constant mechanical power \(P\), and resistive forces are negligible. A motion sensor records the cart's speed \(v\) as a function of its position \(x\) along the track. To determine the power-to-mass ratio \(\dfrac{P}{m}\) from the slope \(S\) of a linear graph, which quantities should be plotted on the vertical and horizontal axes, and what is the value of \(S\) in terms of \(P\) and \(m\)?