Clarification in the definition of force

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Force is defined by Newton's second law as both the rate of change of momentum and the product of mass and acceleration, which are mathematically equivalent under classical mechanics. The proof involves showing that the derivative of momentum (dp/dt) simplifies to mass times acceleration (ma) when mass is constant. However, in the context of special relativity, these definitions diverge, as mass can vary with velocity. The discussion highlights the need to consider relativistic effects when analyzing force. Understanding these distinctions is crucial for accurate applications in physics.
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\According to Newton's second law, force is defined as rate of change of momentum or force is defined as product of mass into acceleration, I both of these definitions are same and right.

My questions are,
(1) how can i prove this two definitions are same?
 
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F=dp/dt=d(mv)/dt=m(dv/dt)=ma
Actually, these two definitions are not equivalent in the framework of special relativity.
 
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