A block of mass \(m\) is projected along a horizontal surface in the \(+x\)-direction with an initial speed \(v_0\) at position \(x = 0\). The coefficient of kinetic friction between the block and the surface increases linearly with position according to \(\mu(x) = \mu_0 \dfrac{x}{L}\), where \(\mu_0\) and \(L\) are positive constants, bringing the block to rest at position \(x_1\). In a second trial, an identical block is projected from \(x = 0\) with an initial speed of \(2v_0\) and comes to rest at position \(x_2\). What is the ratio \(\dfrac{x_2}{x_1}\)?