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These force laws, together with the laws of motion, are the foundations of classical mechanics. They are based on experimental observations and were formulated more than three centuries ago by Isaac Newton (1642-1727).

1st Law of Motion:

An object at rest remains at rest and an object in motion will continue in motion with a constant velocity (that is, constant speed in a straight line) unless it experiences a net external force.
In other words, when the net force on a body is zero, its acceleration is zero. That is, when , then a = 0.

Where F is the force on a body and a is its acceleration.

Newton's first law is sometimes termed simply the "Law of Inertia".
2nd Law of Motion:

Newton stated that the force on a particle is equal to the rate of change of its linear momentum, which is the product of its mass and velocity.

In other words, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. 

Mathematical statement of Newton's second law:

Vector expression:

Component equations
Units of Force and Mass
The SI unit of force is the newton, which is defined as the force that, when acting on a 1-kg mass, produces an acceleration of 1 m/s2. From this definition and Newton's second law, we see that the newton can be expressed in terms of the following fundamental units of mass, length, and time:

Definition of newton: 1 N = 1 kg · m/s2

The unit of force in cgs system is called the dyne and is defined as the force that, when acting on a 1-g mass, produces an acceleration of 1 cm/s2:

Definition of dyne: 1 dyne = 1 g · cm/s2

In the British engineering system, the unit of force is the pound, defined as the force that, when acting on a 1-slug mass, produces an acceleration of 1 ft/s2:

Definition of pound: 1 lb = 1 slug.ft/s2

Since 1 kg = 103 g and 1 m = 102 cm, it follows that 1 N = 105 dynes. It is left as a problem to show that 1 N = 0.225 lb.

The slug is the unit mass in the British engineering system and is that system's counterpart of the SI kilogram.

Units of force, Mass, and Acceleration
System of Units
N = kg · m/s2
dyne = g · cm/s2
British engineering
lb = slug.ft/s2
3rd Law of Motion:

Newton's third law states that if two bodies interact, the force exerted on body 1 by the body 2 is equal to and opposite the force exerted on the body 2 by body 1.

F12 = - F21

In other words, forces always occur in pairs of that a single isolated force cannot exist. The body 1 exerts on body 2 is sometimes called action force; while the force body 2 exerts on body 1 is called the reaction force. In reality, either force can be labeled the action or reaction force. The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and reaction forces act on different objects.

Action-Reaction Force