KINETIC ENERGY


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 than 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 accleration 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 = ½ mV^{2}

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