Question

please tell me the derivation of formula kinetic energy=1/2×mv^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". ThenFirst of all we will find the acceleration of body.Using equation of motion2aS = Vf2 – Vi2 
Putting the above mentioned values 
2ad = V2 – 0
a = V2/2dNow force is given by
F = ma 
Putting the value of acceleration
F = m(V2/2d) 
As we know that 
Work done = FdPutting the value of F
Work done = (mv2/2d)(d)
Work done = mV2/2
OR 
Work done = ½ mV2Since the work done is motion is called "Kinetic Energy"
i.e. 
K.E. = Work done 
OR 
K.E. =1/2mV2.

Answer 2

hii, your answer is here-
K=1/2 mv^2
Hence, m=mass of an object
v=velocity of an object
Note -We know that K=1/2 mv^2
Case 1-If v=Cont.K is directly proportional to m
K1/K2 =M1/M2
Case 2- m=cont.then K is directly proportional to V^2
K1/K2 =V1 ^2/V2^2