3. The principle of work and energy. A particle of mass m moves along a curve under the action of a force F. If the speed of the particle at time t is v(t), its kinetic energy is defined to be mu². Prove that the change in kinetic energy in any time interval is equal to the work done by F during this time interval.
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Solution:
A particle of mass m moves along the curve under the action of force vector F. Let us take a and b are two points in the curve. The work done by the force on the particle is
Let us evaluate the scalar product in the integral
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