Newton's laws of motion

The Newton's first law of motion states ''A body continues to be in the state of rest or constant motion unless it is acted upon by an external agency.''

The Newton's second law states "The acceleration of a particle is directly proportional to the external force applied on it and inversely proportional to the mass of the particle."

The Question that should naturally arise in a student's mind is, if F=0, what is the need to state the first law separately, because it can be deduced from second law that a=0 and hence velocity is constant. So is the first law necessary!?

Ans:-

The measurement of distances and time are done in a reference frame. The first law of motion defines a reference frame where the motion doesn't change unless and otherwise acted upon by an external agency. e.g. you could be in a car that's going along a hillside region of ups and downs and turns. In a reference frame attached to the car, a particle within the car will not remain stationary or in constant motion. So in such a reference frame, the first law is not applicable, and such frame is ruled out in the Newton's scheme of study of dynamics directly. But you could choose a frame fixed to earth say, in which the first law will hold, even if Car moves around. Such a frame where first law holds, is called inertial frame of reference- inertia of a body is maintained. Now again, a frame attached to earth is not infinitely inertial frame of reference, as the earth itself rotates and revolves. for a trajectory of a plane e.g., Earth's frame becomes non-inertial. So you can use a bigger frame at rest w.r.t Sun. But then even it is non-inertial, when you discuss motion of comets, as the Sun moves in the galaxy... So use even bigger frame at the center of galaxy... and finally even bigger in the outer space in between galaxies and galaxy clusters, so that first law is valid in that reference frame.

Either you can keep changing a reference standard for inertial frame, or you can say that so and so part of the space is a good ''local'' inertial reference frame, observed for a so and so interval of time, over which the first law is valid.

In such an inertial frame, second law can be used to calculate the acceleration 'a'.