Question

why 2nd law.of motion called real law of motion

Answer 1

Proof. When we can show that Newton’s first and third law are contained in the second law, then we can say that it is the real law of motion.
(i) First law is contained in second law: According to Newton’s second law of motion,

It means that there will be no acceleration in the body if no external force is applied. This represents that a body at rest will remain at rest and a body in uniform motion will continue to move along the same straight line in the absence of an external force. This corresponds to Newton’s first law of motion. So, first law of motion is contained in Second law of motion
According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.

It means that the linear momentum will change faster when a bigger force is applied.

Consider a body of mass ‘m’ moving with velocity v.

The linear momentum of a body is given by:

p = mv

Now According to Newton’s 2nd Law of Motion:

Force is directly proportional to rate of change of momnetum, that is

F α dp/dt

F  = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

Experimentally k =1

F = k ma

Which is the required equation of force.