Hello,
A particle moves in a straight line with retardation proportional to its displacement. Hence, it's loss of kinetic energy for any displacement x is directly proportional to the square of x, i.e. x^2.
You can check out the mentioned link for the solution:
https://learn.careers360.com/engineering/question-i-need-help-with-this-a-particle-moves-in-a-straight-line-with-retardation-proportional-to-its-displacement-its-loss-of-kinetic-energy-for-any-displacementnbsp-x-is-proportional-to-nbsp/
Hope this helps!!!
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