Question

prove Newtons 2nd law is confined to 1st law of motion mathematically
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Answer 1

Answer:

Newton's First Law of Motion states that a body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.

If a body experiences an acceleration ( or deceleration) or a change in direction of motion, it must have an outside force acting on it. Outside forces are sometimes called net forces or unbalanced forces.

The Second Law of Motion states that if an unbalanced force acts on a body, that body will experience acceleration (or deceleration), that is, a change of speed.

So, Outside forces are sometimes called net forces. If net force acting on a moving body is zero, the body will be at a constant velocity. Thus Newton's first law of motion can be obtained from the second law of motion.