Two identical carts, Cart X and Cart Y, each of mass \(M\), move on a horizontal frictionless track toward a vertical wall with the same initial speed \(v_0\). Each cart is brought to rest by a different spring-loaded bumper. Cart X is brought to rest over a compression distance \(d_X\), and Cart Y is brought to rest over a compression distance \(d_Y\), where \(d_Y < d_X\). The average net force exerted on Cart X during the collision is \(F_X\), and the average net force exerted on Cart Y is \(F_Y\). Which of the following correctly compares the magnitudes of the average forces and provides the best justification using the impulse-momentum theorem?