Question

derive the formula for kinetic energy of an object​

Answer 1

Expression for  Kinetic energy(Ek)- Consider an object with mass m, moving with initial velocity u. Let a force F, act on it causing a displacement s, along the direction of force and accelaration. Let the object attain final velocity v. We know F = m x a ------------------------ 1 By position velocity relation we have, V2 = u2 + 2as or s = v2 -u2 / 2a ----------------------------- 2 The work done by the force W = F x s -------------------------------------- 3 Substituting 1 and 2 in 3 W = (m x a) x (v2 - u2/2a) W = m/2 (v2 - u2) W = 1/2 mv2 - 1/2 mu2 -------------------- 4 For an object to be at rest in the beggining, u = 0 Therefore, W = 1/2 mv2 W = Ek ( Ek = kinetic energy) Therefore, Ek = 1/2 mv2