Question

derive the equation -K.E=1/2mv^2

Answer 1

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.

Answer 2

Explanation:

V²-u²= 2as

V² = 2as ( u = 0 )

V² = 2 F/M × S [ a=F/m ]

F= mv²/2s

W= F × S

W= mv²/2s × s

W= 1/2mv²

W= K.E.

K.E. = 1/2mv²