Derive an expression for kinetic energy using newton's law of motion
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okay.. so.. first of all.. Since it is a form of energy.. it cannot be completely derived from laws of Motion.. we will have to use the formulae of Work
we know that
W= Force.Displacement
also.... from the equations of Motion...
v^2-u^2=2aS
from this equation.. we get the value of Displacement(S) to be v^2-u^2/2a
substituting this in the formula of work..
W= Force . (v^2-u^2/2a)
from Newton's 2nd law..
F=Ma
putting this
W=Ma . (v^2-u^2/2a)
simplifying this we get
W= 1/2 M( v^2-u^2)
we know.. that when work is done... there is change of energy... therefore.. Change in Kinetic Energy = W
hence
∆K.E= 1/2 M(v^2-u^2)
we know that
W= Force.Displacement
also.... from the equations of Motion...
v^2-u^2=2aS
from this equation.. we get the value of Displacement(S) to be v^2-u^2/2a
substituting this in the formula of work..
W= Force . (v^2-u^2/2a)
from Newton's 2nd law..
F=Ma
putting this
W=Ma . (v^2-u^2/2a)
simplifying this we get
W= 1/2 M( v^2-u^2)
we know.. that when work is done... there is change of energy... therefore.. Change in Kinetic Energy = W
hence
∆K.E= 1/2 M(v^2-u^2)
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