FYKOS Year 37 Series 1 Problem 2 — train shifting · FYKOS 37 #37.1.2

Physics · mechanics

Problem

Jarda is standing at the end of the platform, waiting for his train to arrive. When the train's first carriage passes him, he discovers that this is the carriage where he has his seat ticket. At this point, the speed of the train is 8.5 m⋅s−18.5\,\mathrm{m\cdot s^{-1}}, and the train begins to slow down steadily until it stops in 28 s28\,\mathrm{s}. Jarda immediately starts walking in the direction of his carriage, but because he has to push through the crowds of passengers, his speed is only 1 m⋅s−11\,\mathrm{m\cdot s^{-1}}. What is the shortest time the train must stay in the station for Jarda to board his carriage?

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