Question

derive the equation for kinetic energy

Answer 1

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 then 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 f2 – V i2
Putting the above mentioned values
2ad = V 2 – 0
a = V 2 /2d
Now force is given by
F = ma
Putting the value of acceleration
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 = mV2 /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 .


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Answer 2

KE=1/2mv2
M=mass
V=speed
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