Three carts A, B, and C start simultaneously from rest at the origin of a straight, frictionless track. For the first 4.0s each cart experiences a different time-dependent velocity described by
• Cart A: vA(t)=2t
• Cart B: vB(t)=4
• Cart C: vC(t)=8−2t
where velocity is in m/s and time t is in s. The expressions are valid only for 0≤t≤4.0s. After t=4.0s each cart continues to move at whatever constant velocity it has at that instant.
(a) Without performing any explicit calculations, rank the carts by their position relative to the origin at t=4.0s, from farthest right to farthest left. Provide a clear qualitative justification referencing appropriate graphical or conceptual reasoning.
(b) Rank the carts by the magnitude of their acceleration during the interval 0≤t≤4.0s. Justify your ranking.
(c) Determine which cart, if any, comes momentarily to rest during the interval 0≤t≤4.0s, and explain how you arrived at your answer.
(d) Using only reasoning about the motion after t=4.0s, rank the carts by their position relative to the origin at t=6.0s (two seconds after the velocities become constant). Support your ranking qualitatively; no explicit computation is required.