Aman is running at speed c (much less than the speed of light) to catch a bus already at a stop. at t = 0, when he is a distance b from the door of the bus, the bus starts moving with the positive acceleration a. use a coordinate system with x = 0 at the door of the stopped bus.

(a) draw a position vs. time graph for both the man and bus on the same graph. make sure to label what object each curve corresponds to and the initial position of each object in the graph.
(b) what is xman (t), the position of the man as a function of time.
(c) what is xbus (t), the position of the bus as a function of time.
(d) what condition is necessary for the man to catch the bus? assume he catches it at the time tcatch. hint: when are the bus and person at the same position at the same time? (e) find the minimum speed, cmin that the man needs to catch the bus. (f) assume that the man misses getting aboard when he first meets up with the bus. does he get a second chance if he continues to run at the constant speed c > cmin?