where Newtonian mechanics get failed and why?
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The main failures are two:
In reality momentum is not proportional to velocity, but goes as p=γm0v , where m0 is the (rest) mass and γ(v)=1/1−v2/c2−−−−−−−−√ is the Lorentz factor.
In reality, kinetic energy is not proportional to velocity squared, but goes as E=(γ−1)m0c2 .
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