How to derive 1st of motion from second law of motion?
So, if a particle of mass
That means,when no force is acting, a body that was initially at rest i.e
Or,if it was moving with constant velocity
This is the Newton's
That Newton, who was one of the smartest human beings ever to have lived, passed up this chance to cut down his basic laws from three to two - should be an indication that this "proof" is not quite right!
Actually Newton's second law is valid only for a special class of frames called inertial frames. And a frame is inertial only if Newton's first law is valid in it. So, before you apply second law, you have to already make sure that the first law is valid. So, the argument that is often given (wrongly) of the proof of the first law from the second is circular - you can not prove the first law by assuming that it holds to begin with!