Question

Why Second Law Of Motion Is real law of motion ?

Answer 1

Newton's Second Law is that a force gives a corresponding change in momentum. Said mathematically:
\[F = \frac{dp}{dt}\]
Classically, p = mv, and normally mass is constant, we get the familiar result:
\[F = \frac{dp}{dt} = \frac{d (mv)}{dt} = m \frac{dv}{dt} = ma\]

This is the equation of motion because it describes all the changes in motion that result from forces. From this point, we can describe the location of a particle at any time t as a result of a force. Given a little more information, such as the initial position and initial velocity, we can make this description even better.

You may have also learned about inertial reference frames. It turns out that forces act the same in all inertial reference frames. They cause accelerations in one frame just as they would another. Changing frames, however, can change your velocity and position. Therefore, we describe motion based on F=ma, as that's the same in all inertial reference frames.