Sir Isaac Newton First proposed that before he proposed that from the first formula it is easy to prove the second.
From the definition of acceleration and assuming mass to be a constant,
However first of all the books always prove that as because acceleration is directly proportional to force and inversely proportional to mass. From they then prove that
I have a few problems with this. The book starts by saying the following.
They say since mass is a constant it can be moved into the derivative. (Remember the fact that mass is a constant)
From here they conclude that hence we can use the product rule and find force for varying mass (e.g. rockets using up fuel)
this doesn't make sense as in the proof they said mass is constant and that is why u can have . If mass was varying we can't do that. So can someone give me the right proof.
Secondly and lastly, how did Newton show before he showed Newton's Second Law. Whats the proof?