Cyclists A and B start side-by-side at the origin of a straight, level road at t = 0. The positions of the two cyclists as functions of time are qualitatively represented on the same position–time graph described below. For cyclist A, the graph is a straight line with constant slope 3 m/s for the entire 6-s interval shown. For cyclist B, the graph begins with zero slope at t = 0, then the slope steadily increases so that the graph is concave upward; at t = 4 s, cyclist B’s graph intersects and rises above cyclist A’s graph. By t = 6 s, B’s position is 2 m ahead of A’s.
(a) At t = 2 s, which cyclist has the greater instantaneous velocity? Explain.
(b) Estimate the time t_cross at which cyclist B passes cyclist A and describe the reasoning used to obtain your estimate from the graph.
(c) Compare the instantaneous accelerations of the two cyclists at t = 3 s. Provide a qualitative explanation.
(d) Determine which cyclist travels the greater total distance between t = 0 and t = 6 s and justify your answer.