A dynamics cart is placed on a nearly frictionless straight air track. A sensor at the center of the track is chosen as the origin of a one-dimensional coordinate system; positions to the right are positive.
The cart is released from rest at x=+0.50m and rolls left toward a spring bumper located farther to the left. It compresses the spring and reverses direction elastically, then continues to the right until it comes to rest at x=+1.30m. During the motion the cart travels 0.80m while moving left before contacting the spring.
(1) Determine the signed displacement of the cart during the leftward (outbound) leg from release to maximum compression of the spring.
(2) Calculate the signed displacement of the cart during the rightward (return) leg from maximum compression to its final rest position at x=+1.30m. Show how you obtain the value using the coordinate information provided.
(3) Find the cart’s net signed displacement for the entire motion, and separately compute the total distance traveled. Explain why the magnitude of the net displacement differs from the total distance.
(4) Sketch a qualitative velocity–time graph for the cart’s entire trip, clearly indicating the portions of the graph where the velocity is positive, negative, and zero. Label key instants corresponding to release, maximum compression, and final rest. Justify the signs chosen for each portion of your graph.