A cart moves along a straight horizontal track from rest at the origin at time \(t = 0\). An optical sensor records the cart's position \(x\) and speed \(v\), and the position data are well modeled by the equation \(x(t) = c t^{3/2}\), where \(c\) is an unknown positive constant. A student wants to linearize the relationship between \(v\) and \(x\) by plotting a function of \(v\) on the vertical axis and \(x\) on the horizontal axis to determine \(c\) from the slope \(S\) of the best-fit line. Which of the following quantities should be plotted on the vertical axis, and what is the resulting expression for \(c\) in terms of \(S\)?