Serway & Jewett — Motion in One Dimension: Problem 8

A child rolls a marble on a bent track that is 100 cm long as shown in Figure P2.8. We use x to represent the position of the marble along the track. On the horizontal sections from x = 0 to x = 20 cm and from x = 40 cm to x = 60 cm, the marble rolls with constant speed. On the sloping sections, the marble’s speed changes steadily. At the places where the slope changes, the marble stays on the track and does not undergo any sudden changes in speed. The child gives the marble some initial speed at x = 0 and t = 0 and then watches it roll to x = 90 cm, where it turns around, eventually returning to x = 0 with the same speed with which the child released it. Prepare graphs of x versus t, \(v_x\) versus t, and \(a_x\) versus t, vertically aligned with their time axes identical, to show the motion of the marble. You will not be able to place numbers other than zero on the horizontal axis or on the velocity or acceleration axes, but show the correct graph shapes.