25. Kinetic energy If a variable force of magnitude F(x) moves an object of mass m along the x-axis from x1 to x2, the object's ve- locity v can be written as dx/dt (where t represents time). Use Newton's second law of motion F = m(dv/dt) and the Chain Rule dv dx dv dv dx dt dx dt to show that the net work done by the force in moving the object from x, to x, is F(x) dx = =mv;? – mv,?. where vị and v2 are the object's velocities at x1 and x2. In physics, the expression (1/2)mv² is called the kinetic energy of an object of mass m moving with velocity v. Therefore, the work done by the force equals the change in the object's kinetic energy, and we can find the work by calculating this change.

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