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Derivation of 1 ,3 law of motion using 2 law of motion​

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tion:Newton's second law of motion is F=maThat is we have:-F=m(v− tu ) thus, Ft=mv−mu.Now,When F=0, then v=u. That is the absence of force,The object continue to move with same velocitythroughout.Now,when F=0 and u=0, then v=0. That is , an object at rest if no force is acting on it.Thus,Newton's first law is derived from the second law.Now let us consider a system of 2 bodies 1&2 and CONSIDERS that there is no external force acting. Now let F 12 be the force acting on 2 by 1 and F 21 be the force acting on 1 by 2.The RATE of change of momentum of 1= dtdp 1 and rate of change of momentum of 2= dtdp 2 Thus, according to Newton second law of motion F 12 = dtdp 2 and F 21 = dtdp 1 Adding both the above equation, we get:-F 12 +F 21 = dtdp 2 + dtdp 1 =d(p 2 +p 1 )/dtWe know that, no force is applied. Thus momentum change will also be 0 change in velocity occurs.Thus dtd(p 1 +p 2 ) =0Therefore, F 12 +F 21 =0That is F 12 =−F 21 Thus, Newton's third law is proved with Newton's second law.



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