

KINETIC
ENERGY


"Energy
posses by a body by virtue of its motion is referred to as ‘Kinetic Energy’".


FORMULA  
K.E.
= 1/2 mv^{2}



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 mv^{2}  
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
= V_{f}^{2} – V_{i}^{2}
Putting the above mentioned values 2ad = V^{2 }– 0 a = V^{2}/2d 

Now force is given by
F = ma Putting the value of acceleration F = m(V^{2}/2d) As we know that Work done = Fd 

Putting
the value of F
Work done = (mv^{2}/2d)(d) Work done = mV^{2}/2 OR Work done = ˝ mV^{2} 

Since
the work done is motion is called "Kinetic Energy"
i.e. K.E. = Work done OR K.E. =1/2mV^{2}. 

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