Consider a system of two toy rail cars (i.e., frictionless masses). Suppose that car 1 has mass 6 kg and is traveling at 3 m/s toward the other car. Suppose car 2 has mass 3 kg and is moving toward the other car at 9 m/s. There is a bumper on the second rail car that engages at the moment the cars hit and does not let go (it connects the two cars). The bumper acts as a spring with spring constant 6 N/m. The second car is 10 m from a wall. Let t = 0 be the time that the cars link up. Let x1 be the displacement of the first car from its position at t = 0, and let 2 be the displacement of the second car from its original position. a. Set up a system of second-order differential equations that models this situation. x" = The crash of two rail cars. 10 meters x(0) = = meters y(0) = meters r'(0) = meters/second y'(0) = meters/second b. Find the solution to this system of differential equations. x(t) = y(t)= meters meters c. Will the cars be moving toward the wall, away from the wall, or will they be nearly stationary? ? ? toward the wall away from the wall they will remain stationary