derive expression for kinetic energy

The equation of kinetic energy can be acquired from the equation of motion. Let us assume that an object of mass m is initially at rest and in time t it moves with velocity of v. Consider that the distance covered by the object is s thus from we know that distance s is related to average velocity and time as follows, s=vav×t That is, s=v−u2×t As initially the object is at rest, therefore we get, s=vt2 Newton’s second law of motion says that, F=ma As, a=vttherefore we get, F=mvt The work done by any object is defined as the product of force and the displacement, therefore we have, W=mvt×vt2W=12mv2 Therefore, according to the definition of kinetic energy the net work done is the change in kinetic energy of the object, therefore have, KE=12mv2