# Show that work done by a force on an object is equal to the change in KINETIC ENERGY of the object.You could explain with formula derivation

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Potential energy and kinetic energy always have a trade off. The two of them combined together give one hundred percent of the energy contained in the system. The best example I can think of is a roller coaster, where work is done on the roller coaster car when it slowly is pulled up that first hill. As it is pulled by the mechanism up the hill, work is being performed on it, which will be stored as potential energy. The formula for potential energy is PE = mass times gravity times height. As the car starts down the first hill, the potential energy stored up in the car starts converting over to kinetic energy, energy of motion. The formula for kinetic energy is 1/2 mass times velocity squared. At approximately half way down the hill, there should still be 50% potential energy, 50 percent kinetic energy. At the bottom of the hill, there should be 0% potential energy and 100% kinetic energy. At all times, the total between the two is equal to the amount of work done to build the energy up to begin with.