Why 2nd law is actual law of motion
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The first law has already given us a qualitative definition of force. Now we are interested in finding out its magnitude. According to Newton’s second law of motion, the net force experienced by a body is directly proportional to the rate of change of momentum of the body. It can be written as:f ∝ dP/dt⇒f ∝ (mv−mu)/t⇒f∝m(v−u)/t⇒f∝ma⇒f=kmaWhere k is the constant of proportionality and it comes out to be 1 when the values are taken in SI unit. Hence the final expression will be,F = ma