Question

Plz tell me the ..
Q. Derivation of kinetic energy?
Q. Derivation of conservation of energy?

class 9..
Ch 11 work and energy...
Science​

Answer 1

Answer:

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• Derivation of kinetic energy

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Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Derivation:

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

Let A force F acts on the object which moves the object through a distance S.

The workdone=F×S

W=Fnet × 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

=½m(v² - u²)

As we assumed object at rest, u=0

KE= ½mv²

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.

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• Derivation of conservation of energy

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The equation expressing conservation of energy is:

KEi+PEi=KEf+PEf.

If you know the potential energy for only some of the forces, then the conservation of energy law