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Question
Derive kinetic energy?
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Solution
Derivation of the equation of Kinetic Energy:
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S = v2 - u2 / 2a
We know F = ma. Thus using above equations, we can write the work done by the force, F as
W = ma × v2 - u2 /2a
or
W = 1 / 2 m(v2 - u2)
If object is starting from its stationary position, that is, u = 0, then
W = 1 / 2 m v2
It is clear that the work done is equal to the change in the kinetic energy of an object.
If u = 0, the work done will be W = 1 / 2 m v2.
Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S = v2 - u2 / 2a
We know F = ma. Thus using above equations, we can write the work done by the force, F as
W = ma × v2 - u2 /2a
or
W = 1 / 2 m(v2 - u2)
If object is starting from its stationary position, that is, u = 0, then
W = 1 / 2 m v2
It is clear that the work done is equal to the change in the kinetic energy of an object.
If u = 0, the work done will be W = 1 / 2 m v2.
Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2
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