Newton's First law:-
Every body continues to be in its state of rest or of uniform acceleration in a strraight line unless compelled by some external force to act otherwise.
Newton's Second law:-
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
from the statement of 2nd law, it is possible to derive expression that relates force and acceleration :- F = dp/dt = ma
F - force, p - momentum, a - acceleration, m- mass ( F, p and a are vector).
First law of motion can be expressed as follows:-
If the net external force on a body is zero, its acceleration is zero. Acceleration can be non-zero only if there is a net external force on the body. The same interpretation can be infered from second law. If force F is zero then acceleration a =0. Hence if the resultant force on a body is zero, then acceleration is zero and the body moves with constant velocity, as stated by the first law.
Newton's thrid law:-
To every action, there is always equal and opposite reaction.
A simple and clear way of stating third law is :- Forces always occur in pairs. Force on a body A by B is equal and opposite to the force on the body B by A.
Many physical pheneomena demands the knowledge of reaction force. Some of the examples are thrust generated for rocket upward motion, inertial confinement in thermo nuclear fusion etc. But we need to workout the action force using second law and thereby we get the direction and magnitude of reaction force.
For example when a billard ball hit the wall and reflected back, if we need to know the force on wall due to the ball, first we need to calculate the change in momentum for the ball after reflection and get the force using second law during a contact time Δt. Then by using third law we know the force of same magnitude but in opposite direction acts on the wall.