Respuesta :
Answer:
Work-Energy Theorem is that the work done on an object is equal to the change in the kinetic energy of that object:
[tex]W = \Delta K = K_2 - K_1 = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2\\ Fx = \frac{1}{2}m(v_2^2 - v_1^2)[/tex]
The relation between velocity and position is derived from the kinematics equations:
[tex]v_2^2 = v_1^2 + 2ax\\x = \frac{v_2^2 - v_1^2}{2a}[/tex]
If we plug x into the work energy theorem, Newton's Second Law can be found:
[tex]Fx = \frac{1}{2}m(v_2^2 - v_1^2)\\F\frac{v_2^2 - v_1^2}{2a} = \frac{1}{2}m(v_2^2 - v_1^2)\\F = ma[/tex]
Newton's First Law is the law of inertia: If the net force on an object is zero, the acceleration of the object is also zero.
If the acceleration of the object is zero the kinematics equation yields:
[tex]v_2^2 = v_1^2 + 2ax = v_1^2 + 2*0*x = v_1^2\\v_2 = v_1[/tex]
Then if we plug this into the work energy theorem
[tex]Fx = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2[/tex]
[tex]Fx = 0\\F_{net} = 0[/tex]
