Question

Prove tha kinrtic energy of a body m moving with velocity v is given
Ek=½mv²

Answer 1

kinetic energy is the energy possed by an object when a body is in motion

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.

hope it helps
plse mrk as brainliest

Answer 2

let a body is moving with a acceleration 'a' and started with initial velocity U reached to final velocity V and covered a distance S.
so ,from third equation of motion
V square = u square + 2 as
V square - u square = 2 as
(V squared - u square)/ 2a=s
so it means,s=v2-u2/2a (1)
now you know that ,w= f×s
w=m×a×s
putting the value of 's' from (1) ,
w=ma×v2-u2/2a
w=m×v2-u2/2
now we know that the object is started with the initial velocity zero so the value of u will be zero
putting the value of u=0
w=mv2/2
Ek=1/2×mv2