Question

derive an expression of kinetic energy of an object​

Answer 1

Let us consider an object of mass m which is at rest lying on a table.

Let a force F act on the object which makes the object move through a distance s.

Then work done = F×s

W=F×s-------(1)

Let the work done on the object causes a change in its velocity from u to v and let a be the acceleration.

From Third equation of motion:

v²−u²=2as

s=V²−u²/2a----------(2)

By Newton's Second law:

F=ma------(3)

From equation (1), (2) and (3)

W=ma×(v²−u²/2a)=(1/2)m(v²−u²)

As we assumed object at rest, u=0

W=(1/2)mv²

we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.

K.E.=½mv²

Reference from Toppr