Question

derive the expression for kinetic energy (ke)​

Answer 1

Answer:

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Let a body of mass ‘m’ is moving with a velocity ‘v’.A force ‘F’ is applied on it to stop its motion for which the retardation ‘h’ is produce in the body and the body covers a distance ‘s’ before coming rest.

Work done by the force to stop the motion of the body is the measure of kinetic energy .

Here,

Initial velocity = v

Final velocity = 0(zero)

From Newton’s 2nd law

F = ma

or, a = F/m

From 3rd equation of motion

0=v^2 - 2as

or, 2as = v^2

or, 2 × F/m × s = v^2

or, s = (mv^2) /2F

Therefore , workdone by the force,

W = Fs

or, W = F ( mv^2 )/2F

or, W = 1/2 mv^2

Hence,

Kinetic energy = 1/2mv^2.

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Answer 2

Explanation:

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)=(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=1/2mV²  

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