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Two people, who are traveling on a bullet train between Tokyo and Kyoto, are willing to tolerate acceleration magnitudes as large as 0.2 g. The driver wants to change speeds from 250 to 300 km hr-1 on a curved piece of track. If the radius of curvature of the piece of track is 5 km, what is the minimum time the driver can use to change speeds?

For this question I am assuming that the angular acceleration is constant and that at the point where the tangential velocity is maximum (300Km/hr) the acceleration is 0.2g. I know I will get a smaller time if I consider the total acceleration to be the same during the whole trip. Any suggestions on how to solve this problem.

Thank you

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