Math Solution of Laws of Motion

Newton’s laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces. They have been expressed in several different ways over nearly three centuries, and can be summarized as follows:

First law: If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.

Second law: The acceleration a of a body is parallel and directly proportional to the net force F acting on the body,

is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma.

Third law: When a first body exerts a force F1 on a second body, the second body simultaneously exerts a force F2 = −F1 on the first body. This means that F1 and F2 are equal in magnitude and opposite in direction.