Question

derive an expression for kinetic energy possesed by an object of mass m moving with velocity v.

related answers ONLY. unrelated or wrong ones will be reported. thank you. ​

Answer 1

Answer:

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=F

net

×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×(V

2

−u

2

/2a)=(1/2)m(V

2

−u

2

)

As we assumed object at rest, u=0

W=(1/2)mV

2

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=1/2mV

2

Answer 2

★ Expression For Kinetic Energy possessed by an object : -

Consider a body of mass ‘m’ moving with a velocity ‘v’ and Let the Force ‘F’ act on the body.

So , The Work done can be defined as :

$: \implies \: Work = Force \times displacement$

$: \implies \: W = F \times S$

Where ,

• W » Work done due to the external force.
• F » Force acted on the object.
• S » Displacement of the object due to force.

So, According due Newton's Second law of motion, We know that

$: \implies \: F= ma \:$

Where ,

• F » Force acting on a body.
• m » mass of the body.
• a » Acceleration of the body.

By substituting [ F = ma ] in the work done equation , we get

$: \implies \:W=maS \: \: \: \: \: \: \: \: \: \: \: \: - (1)$

Then , By Third Equation of motion , We know that

$: \implies \: {v}^{2} = {u}^{2} + 2aS$

Initially the body is at rest , So u = 0 ,

$: \implies \: {v}^{2} = 2aS$

$: \implies \: aS = \dfrac{1}{2} {v}^{2} \: \: \: \: \: \: \: \: \: \: \: - (2)$

Substituting equation (2) in (1) , we get

$: \implies \: W = \dfrac{1}{2} m {v}^{2}$

Therefore The Kinetic Energy of the particle is

$: \implies \: \bf \: K.E = \dfrac{1}{2} m {v}^{2}$

So what's Kinetic Energy ?

★ The energy possessed by an object due to it's motion , we call it as Kinetic energy. That's why we take work done as K.E. The SI unit of Kinetic Energy is Joules ( J ) .

If We are given with mass and Velocity , We can calculate the Kinetic energy of the particle possessed.