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Happiness

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where ##g## and ##\alpha## are positive constants.

Can you show that ##v_f<v_0## for all positive values of ##v_0## using a non-graphical method?

Physically, ##v_0## and ##v_f## are the initial and final speeds (at the same height) of a ball thrown upwards in a medium with a drag force ##F=-m\alpha v##.