prove the formula K.E.=1/2mv2
K.E. = 1/2 mv2
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".
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. |