I can't understand how its solved.

Dear student
please find simple and easy method for derivation of kinetic energy. I hope it helps you
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

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