Force
Force is the action that accelerates a body having mass. A force is a vector quantity, having a magnitude and a direction that corresponds exactly to the direction of its resulting acceleration. Forces from different sources acting on the same body sum as vectors to form a net force or resultant force on the body. A body's acceleration is proportional to the net force exerted it and, according to Newton's Second Law of Motion, the proportionality constant is the mass of the body. There are two useful expressions for the Second Law:
and
Here m, v, a, and p are the mass, velocity, acceleration, and momentum respectively of the body upon which the force is exerted. When a body experiences a nonzero net force for any period of time, its velocity and momentum change over that time. Calculus is required to model the functional relations between these physical quantities, although models for forces are typically introduced to students through average quantities to simplify the analysis.
Laws of Motion
The physical laws that Newton presented in his Principia are sufficient to introduce the most universal features of force and its effect on bodies.
According to Newton's First Law of Motion, the velocity of a body is constant when the net force exerted upon that body is zero. Whether the velocity is zero or nonzero has no bearing on its constancy in the absence of a net force. Historically, this constancy had been attributed to a vis insita or internal force that maintains the body's state of rest or motion but today it is understood that motion is only relatively distinguishable from rest and this constancy is a well-established law without deeper explanation. Despite its simplicity, this constancy correlates with the resistance of a body to change in its motion - known more technically as inertia - and has a significant place in the general theory of relativity.
As already stated, the Second Law expresses how the force on a body is proportional to its resulting acceleration by its mass.