Prove that newton's second law of motion is the real law

We shall derive the 1^{st} and the 3^{rd} law of motion fron the 2^{nd} law.

Derivation of 1^{st} law:

According to Newton’s 2 ^{nd }law of motion,

F = ma

Where, F is the force applied, m is the mass of the body and a is the acceleration of the body.

So,

In absence of a force,

F = 0

=> ma = 0

=> a = 0

Since, m cannot be zero for a body.

Zero acceleration means, body at rest will remain at rest and a body in uniform motion will continue its uniform motion. Which is Newton’s 1 ^{st }law of motion.

Derivation of 3^{rd} law:

Consider an isolated system of two bodies A and B. An isolated system is such that no force acts on the system.

This is the Newton’s third law of motion for a body exerting some force on another.

Thus, Newton’s 2^{nd} law of motion is the most basic law of motion.

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