Cart 1 of mass \(m\) and Cart 2 of mass \(2m\) travel along a horizontal frictionless track with the same initial linear momentum of magnitude \(p_0\). Each cart is brought to rest by a bumper that exerts a retarding force of magnitude \(F_1(t) = F_{\text{max}, 1} \sin\left(\dfrac{\pi t}{\Delta t}\right)\) over the interval \(0 \le t \le \Delta t\) on Cart 1, and \(F_2(t) = F_{\text{max}, 2} \sin\left(\dfrac{\pi t}{2\Delta t}\right)\) over the interval \(0 \le t \le 2\Delta t\) on Cart 2. Which of the following correctly compares the peak retarding forces, \(F_{\text{max}, 1}\) and \(F_{\text{max}, 2}\), and the magnitudes of the net work done on the carts, \(|W_1|\) and \(|W_2|\), during their respective stopping processes?