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To derive a mathematical equation for kinetic energy, let us consider an object having mass m moving with an initial velocity u. F is the force which acts on the object and displaces it by a distance s in the same direction. Therefore, work done is W = Fs
As we see, there is an external force acting on this object, an acceleration ‘a’ is produced which will change the velocity of an object from initial velocity u to a final velocity v. According to the equation of motion, we can write,
v^2 - u^2 = 2as
s = ( v^2 - u^2 )/2a
From the second law of motion, we know that F = ma. Substituting the values of F and s in the equation W = Fs, we get
W = (ma)((v^2 - u^2)/2a)
W = ½m(v^2 - u^2)
If the object starts from rest, then u = 0. Therefore, W = ½ mv^2 This shows that work done on an object is equal to the change in its kinetic energy. Kinetic energy possessed by an object m and moving with a uniform velocity v is given as
Ek = ½ mv^2
The equation for kinetic energy is thus universally given as
KE = ½ mv^2
Where, m = mass (kg), v = velocity (m/s), KE = Kinetic energy (J).
