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The bee and the braking train

kinematicsrelative-motionclassic-variant

A train enters a station at 50 m/s and brakes with uniform deceleration, coming to a complete stop exactly at the end of the platform, 500 m from the entrance. At the instant the train enters, a bee takes off from the buffers at the end of the platform and flies straight towards the train at 40 m/s. When it reaches the front of the train it turns round and flies back to the buffers, then back to the train, and so on, until the train stops and the bee is crushed against the buffers.

How far does the bee fly in total?

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Do not add up the legs. Find how long the whole thing takes.

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