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I'd like to get back to the original question for a moment. As I
understand it you have an observer on a moving train who is looking at
tree someplace on the ground. The observer on the train calculates the
K.E. of the tree. The train is then decelerates to a stop, and the
observer calculates the K.E. of the tree again and finds that it is zero.
Someone then wanted to know where the lost K.E. went.
My naively classical mind said that it didn't go anywhere - that
the observer on the train decelerated so the change in KE was not measured
in an "inertial" frame so it was a physically meaningless number.