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Newtons laws of motion:

1.An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.

2.The acceleration of an object depends on the mass of the object and the amount of force applied.

3.Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

What exactly did Newton do to prove his statements? Did he give a mathematical proof or was it experimentally based? Why did so many people accept that his statements will always hold true?

I am so sorry if my question offends you. It's just that I don't know much about the history.

Connor Behan
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Let's leave aside the history of Mechanics and let's concentrate on the structure of any Physical law. Physics is about the real world. In practice, this statement means that at variance with Mathematics, we are not entitled to choose the starting point (axioms in mathematics) of any physical theory at our will.

The meaning of Principle in physics is that it is a statement directly or indirectly based on many experiments. Therefore, there is nothing like a mathematical proof. However, it is also not necessary that there direct experiments confirming the principles. It is enough that the consequences extracted from the principles agree with the experiments.