How to derive 1st and 3rd laws of motion from 2nd law?

manpreet Best Answer 2 years ago

Newton's second law of motion is F = MA. Thus, Ft = mv - mu. Now, when F = 0, then v = u. In the absence of force, the object continues to move with same velocity throughout. Now, when F = 0 and u = 0, then v = 0. That is, an object at rest will remain at rest if no force is acting on it. Thus, Newton's first law is derived from second law. Now, let us consider a system of 2 bodies 1 and 2, and consider that there is no external force acting. Now, let F12 be the force acting on 2 by 1 & F21 be the force acting on 1 by 2. The rate of change of momentum of 1 = dp1/dt and rate of change of momentum of 2 = dp2/dt. Thus, according to Newton's second law of motion F12 = dp2/dt and F21 = dp1/dt Adding both the above equations, we get F12 + F21 = dp2/dt + dp1/dt = d(p2+p1)/dt We know that, no force is applied. Thus, momentum change will also be 0 because no change in velocity occurs. Thus, d(p1 + p2)/dt = 0 Therefore, F12 + F21 = 0 That is, F12 = - F21. Thus, Newton's third law is proved with Newton's second law.