What is Kinetic Energy?
The kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Kinetic energy depends on the velocity and mass of the body. If the velocity of an object is zero then its kinetic energy is also zero.
Let us try to derive the expression for kinetic energy.
Derivation: Formula of Kinetic Energy
Consider an object of mass ‘m’ at rest. Suppose a force ‘F’ is applied to this body such that it is displaced by a distance ‘s’ and reaches a velocity ‘v’.
The work done on the body ‘W’ will be given as,
W = F ✕ s
Force ‘F’ can be written as,
F = m ✕ a
Thus, the work done will be equal to,
W = ma ✕ s
We also know the equations of motion and according to the third equation of motion,
𝒗𝟐 − 𝒖𝟐 = 𝟐𝒂𝒔 Or 𝒂𝒔 = (𝒗𝟐−𝒖𝟐)
𝟐
Now, on substituting the value of ‘as’ in the equation of work done, we get,
W =𝒎 (𝒗𝟐−𝒖𝟐)
𝟐
Since, the body was at rest, ‘u’ will be zero. Also the work done is nothing but equal to the change in kinetic energy we can substitute ‘W’ by ‘K.E.’
K.E. =𝒎𝒗𝟐
𝟐
Hence an object of mass m moving with uniform velocity v possess Kinetic energy equals to,
K.E. = 𝒎𝒗𝟐