What does the work - kinetic energy theorem imply ?

Explanation

(i) It states that work done by the force acting on a body is equal to the change produced in the Kintic Energy of the body.
(ii) Consider a body of mass m at rest on a frictionless horizontal surface.
(iii) The work (W) done by the constant force (F) for a displacement (S) in the same direction is ,
`W =Fs " ""............"(1)`
The constant force is given by the equation
`F= ma" "".............."(2)`
The third equation of motion can be written as,
`v^2=u^2+2as`
`a= (v^2-u^2)/(2s)" ""............."(3)`
Susbtituting for a in equation (2),
`F= m ((v^2-u^2)/(2s))" ""..............."(4)`
Substituting equation (4) in (1),
`W=m((v^2)/(2s)s)-m ((u^2)/(2s)s)`
`W= (1)/(2)mv^2-(1)/(2)mu^2" ""................."(5)`
The expression for kinetic energy :
(i) The term `((1)/(2)mv^2)` in the above equation is the kinetic energy of the body of mass (m) moving with velocity (v).
`KE= (1)/(2)mv^2" ""............"(6)`
(ii) Kinetic energy of the body is always positive. From equations (5) and (6)
`triangleKE = (1)/(2) mv^2 -(1)/(2) mu^2" ""............"(7)`
Thus, `W= triangleKE`
(iii) The expression on the right hand side (RHS) of equation (7) is the change in kinetic energy `(triangleKE)` of the body.
This implies that the work done by the force on the body changes the kinetic energy of the body.
This is callled work -kinetic energy theorem.