Question

Derive an expression for the mathematical formulation of the second law of motion.​

Answer 1

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system.

Force applied is directly proportional to the product of mass and acceleration .

Let  be the initial and final momentums respectively.

According to newton's second law :-

pf - pi / t ∝ F

We know that, Momentum ( P) = mv .

Let v be the final and u be the initial velocity .

Now,

mv - mu / t ∝ F

F ∝ m ( v-u) /t

F ∝ ma.

F = k ma.

Here, K is the proportionality constant. It's value is 1 .

Units of Force are given by the units of mass and acceleration. Units of force is Kgm/s² .

In accordance to honour the contributions of Newton, 1 kgm/s² is termed as 1 Newton.

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Answer 2

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. Force applied is directly proportional to the product of mass and acceleration . Let be the initial and final momentums respectively. We know that, Momentum ( P) = mv .