Question

proof kinetic energy​

Answer 1

K.E. = 1/2 mv2

Kinetic energy depends upon the mass and velocity of body. 

If velocity is zero then K.E. of body will also be zero. Kinetic energy is a scalar quantity like other forms of energies. DERIVE: K.E = 1/2 mv2 

PROOF

 Consider a body of mass "m" starts moving from rest. After a time interval "t" its velocity becomes V.

If initial velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body is "d". Then

First of all we will find the acceleration of body.Using equation of motion

2aS = Vf2 – Vi2 

Putting the above mentioned values 

2ad = V2 – 0

a = V2/2d

Now force is given by

F = ma 

Putting the value of acceleration

F = m(V2/2d) 

As we know that 

Work done = Fd

Putting the value of F

Work done = (mv2/2d)(d)

Work done = mV2/2

OR 

Work done = ½ mV2

Since the work done is motion is called "Kinetic Energy"

i.e. 

K.E. = Work done 

OR 

K.E. =1/2mV2.

Answer 2

As

Work done= Force × Displacement

W=Fs------(1)

Using the 2 law of motion

F=ma--------(2)

Now by using 3 equations of motion

${v}^{2} = {u}^{2} + 2as$

$s = \frac{ {v}^{2}-{u}^{2} }{2a}$

---------(3)

Putting both the values of equations (2) and (3) in equations (1)

$w = ma \frac{ {v}^{2} - {u}^{2} }{2a} \\ w = \frac{1}{2} m( {v}^{2} - {u}^{2} )$

When initial means u=0 then formula will be

$w = \frac{1}{2} m {v}^{2}$

As Kinetic energy is stored in the form of work done the

W=K.E.

So,

$k.e. = \frac{1}{2}m {v}^{2}$

Hence proved

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