Three motorized carts P, Q, and R move along a straight horizontal track. A position–time representation is obtained for each cart over the same 10 s interval. The graphs are straight-line segments, and the following information is extracted:
• Cart P moves from x=0m at t=0 to x=20m at t=10s.
• Cart Q moves from x=−10m at t=0 to x=10m at t=10s.
• Cart R moves from x=5m at t=0 to x=35m at t=10s.
Assume each cart moves with constant velocity during the 10 s interval.
(a) Rank the carts by the magnitude of their velocity during the 10 s interval, from largest to smallest.
(b) Identify which cart(s), if any, have a negative velocity during the interval and explain how you can tell from the given information.
(c) Each driver looks only at the position–time graph to decide whether to speed up. Describe how the slope of the graph allows the driver to determine whether the cart is moving faster or slower than another cart.
(d) Immediately after t=10s, identical braking systems are applied to all three carts, producing a constant deceleration that brings every cart to rest in exactly 4.0s. Rank the magnitudes of the braking acceleration experienced by the three carts, and justify your answer without explicit numerical calculation.