# derivation of work energy theorem for constant force

__Work-Energy Theorem:__

- The energy associated with the work done by the net force does not disappear after the net force is removed (or becomes zero), it is transformed into the Kinetic Energy of the body. We call this the Work-Energy Theorem.

- If the body's speed increases, then the work done on the body is positive and we say its Kinetic Energy has increased. Whereas if the body's speed decreases then it kinetic energy decreases and the change in kinetic energyDKEis negative. In this case the body does positive work on the system slowing it down or alternately the work done on the body is negative.

- If the object is not rigid and any of the forces acting on it deforms the object, then the Work-Energy Theorem will no longer be valid. Some of the energy transferred to the object has gone into deforming the object and is no longer available to increase or decrease the object's Kinetic Energy.

Frame of Reference:

Direction of the Net Force.

Start with Newton 2^{nd}Law for one-dimensional motion:

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Next use the Equations forConstant Accelerationthat does not involve time:

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Calculate the Net Work using the above relationships:

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Many problems you encounter related to Work and Energy will have constant forces. While you are trying to learn how to use the concepts of Work and Energy, avoid using Newton's Second Law to solve these problems or else you will have missed the opportunity to learn how to use Work and Energy to solve them. It is reasonable to use the Second Law approach as a way to double-check your Work-Energy solutions.