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If i run down some stairs and stop, what happens to your kinetic energy and your initial gravitational potential energy?

Answer 1

Examine the two forms of energy you are referring to first:

Kinetic Energy depends on the mass and speed of the object #KE=1/2mv^2# while Gravitational Potential Energy depends on the mass and position of the object #U_g# #= mgh#.

So in your example, by coming to a stop your kinetic energy becomes zero. Because your height decreased, your potential energy also decreases (whether it equals 0 or not depends on where you define 0 #U_g# to be.)

You have transformed all of the energy you "lost" into heat, sound, and internal energy.

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Answer 2

Sebastian Acosta

When you run down some stairs and stop, your kinetic energy decreases while your initial gravitational potential energy decreases.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.