How can Newton's first law be derived from newtons second law?

Answer 1

Newton's 1st Law: If F = 0 then object is at rest or in a uniform rectilinear motion.

Newton's 2nd Law: F = ma.

Starting from Newton's second Law: F = ma, if F = 0 then a = 0 then v = constant. then the object is either at rest (v = 0 = constant) or in a uniform rectilinear motion (v=constant).

This is what is widespread, but wait...

Newton is not stupid! If his First Law could be derived from his second law, so why he stated it as separate law?!

There is a common misconception about Newton's first law. The correct statement of Newton's first law is:

"In the absence of forces, it is possible to specify a frame of reference where the object is either at rest, or in a uniform rectilinear motion. This frame of reference is called inertial frame of reference".

Notice that! Newton's first law central point is to define inertial frame of reference, and guarantee that such frame exists.

Absolutely, There is no way to derive this from newton's second law.

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Newton's 1st Law is derived from the 2nd Law F=ma, by setting F to zero, 0=ma,

thus a=o/m or no force, no acceleration.