The second law, which states that rate of change of object's momentum is proportional to the force exerted upon it is the most practical law. This law is the logical continuation of the inertia law and explanation of Galileo's principle and transformations. Second law gives a prediction to what will happen with the object when a force acts on it: object's velocity will change and object will accelerate (with negative or positive acceleration). In order to understand the meaning of this law, mass is introduced. The mass of the object is a quantitative measure of inertia, which defines amount of matter contained in object. That's why in modern interpretation the second law says that objects acceleration is directly proportional to the magnitude of the total force and inversely proportional to the mass of the object. That's why mass of the object also defines object's resistance to acceleration.
In terms of mathematics, second law can be written as a differential equation:
where F. is force, k is proportionality coefficient, v is objects velocity and m is object's mass.
If a is acceleration is a constant,...
Third law is mathematical conclusion of the law of conservation of momentum (as it can be stated that acceleration is a derivative of velocity and force is a derivative of momentum). Third law states that though forces of interaction are equal, accelerations may be different as masses of objects may be not the same.
Laws of Newton were proved more than 200 years ago on the base of everyday experiments and they serve as excellent approximation to kinematics and dynamics of objects in everyday life. These laws form the basis of classical mechanics, or mechanics of idealized macro world. They can be applied without errors to objects, which have speeds much smaller than relativistic speeds (speeds which are close to the speed of light). But even in relativistic world the form and essence of Newton's laws is preserved if relativistic space transformations are followed. http://en.wikipedia.org/wiki/Newton's_laws_of_motion
Newton's three laws of motion
