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 mv²....

Extracted text: 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 mv². Prove that the change in kinetic energy in any time interval is equal to the work done by F during this time interval.