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A man 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 to 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.

What is x_{\rm man}(t), the position of the man as a function of time?
Answer symbolically in terms of the variables b, c, and t.

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