prove that change in kinetic energy of a particle is equal to the work done on it by a variable force
The work-energy theorem states that the work done on a body is equal to the change in kinetic energy of the body.
Suppose a body of mass ‘m’ is under an acceleration ‘a’ due to which its initial speed ‘u’ at time t = 0 becomes final velocity ‘v’ at time t = t.
The distance travelled by the body in this time can be found out using,
v2 = u2 + 2as
Multiplying both side by ½ m we have,
½ mv2 = ½ mu2 + mas
= > (ma)s = ½ mv2 – ½ mu2
[Force on the body = ma]
= > Work done = change in kinetic energy of the body