# Derive the expression for kinetic energy of
body of mass m in mowing with velocity v
Answers
ANSWER
Kinetic Energy:
The energy possessed by an object due to its motion is called as kinetic energy.
Derivation:
Let us consider an object of mass "m" which is at rest on smooth horizontal plane.
Let a Force ,F acts on the object and let the object from rest moves from point A to point B and covers a displacement S.
The Work done by Force on the object is :
Workdone = Force x displacement.
W=F×S ____(1).
From third equation of motion;
V
2
−U
2
=2aS
S=
2a
V
2
−U
2
______(2)
By Newtons second law of motion:
F=ma
From equation 1 and 2
W=
2a
m∗a∗(V
2
−U
2
)
As we have assumed object is at rest, U=0
W=
2
mV
2
The Work Done appears as kinetic energy of the body.
Therefore,
K.E=(
2
1
)mV
2
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Since we know that,
The dimension of energy [E]=[M
1
L
2
T
−2
]
The dimension of mass [M]=[M
1
L
0
T
0
]
Dimension of velocity[V]=[M
0
L
1
T
−1
]
Let [E]=k[M]
x
[V]
y
Where k is the proportionality constant which is a dimensionless quantity.
Therefore,
[M 1 L 2 T −2 ]=k[M 1 L 0 T 0 }x [M 0 L 1 T −1 ] y
So, x=1,y=2
Thus, We have
E=kmv ²
It is found that k= ½
Hence, E= ½ mv²
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