Newtons Laws of Motion

I #

In an intertial frame of reference (i.e. a frame of reference undergoing zero acceleration), an object at rest stays at rest (or, similarly, keeps its initial velocity) unless acted upon by an outside force.

∑F=0⇔dvdt=0

II #

In the simplest of terms:

F=ma

which states that

The vector sum of the forces on an object is equal to that objects mass times the acceleration

where m is assumed as a constant.

In terms of infinitesimal change, the same law is seen as

F=mdvdt=ma

III #

When one body exerts a force on another body, the second body exerts an equal force in the opposing direction

Fa=−Fb