Newton's first law of motion is often stated as: "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force"
There are two clauses or parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects.
The math problem
Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when:
The container was at rest and you attempted to move it
The container was in motion and you attempted to stop it
The container was moving in one direction and you attempted to change its direction.
The water spills whenever the state of motion of the container is changed. The water resisted this change in its own state of motion. The water tended to "keep on doing what it was doing."
Newton's second law of motion can be formally stated as: "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object."
NEWTON'S SECOND LAW OF MOTION PERTAINS TO THE BEHAVIOR OF OBJECTS FOR WHICH ALL EXISTING FORCES ARE NOT BALANCED. THE SECOND LAW STATES THAT THE ACCELERATION OF AN OBJECT IS DEPENDENT UPON TWO VARIABLES - THE NET FORCE ACTING UPON THE OBJECT AND THE MASS OF THE OBJECT. THE ACCELERATION OF AN OBJECT DEPENDS DIRECTLY UPON THE NET FORCE ACTING UPON THE OBJECT, AND INVERSELY UPON THE MASS OF THE OBJECT. AS THE FORCE ACTING UPON AN OBJECT IS INCREASED, THE ACCELERATION OF THE OBJECT IS INCREASED. AS THE MASS OF AN OBJECT IS INCREASED, THE ACCELERATION OF THE OBJECT IS DECREASED.
This verbal statement can be expressed in equation form: a = Fnet / m
The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration: Fnet = m • a
1 Newton = 1 kg • m/s2
The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.
Newton's third law is: "For every action, there is an equal and opposite reaction."
The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite action-reaction force pairs.
A variety of action-reaction force pairs are evident in nature. Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. But a push on the water will only serve to accelerate the water. Since forces result from mutual interactions, the water must also be pushing the fish forwards, propelling the fish through the water. The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make it possible for fish to swim.
The Physics Classroom http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law