Newton’s 1st law:

Every body persists in a state of rest or of uniform motion along a straight line (i.e. with constant velocity) unless and until it is acted upon by an external force to change that state.

Let us consider, \( \vec{F} \) be the vector sum of all the external forces acting on a particle and \( \vec{a} \) be the acceleration of that particle. So Newton’s 1^st law can be written as,

\( \vec{a}=0 \) if and only if \( \vec{F}=0 \)

This above statement can be described in two ways:

• When the vector sum of the forces acting on the particle becomes zero, then we can surely say that the particle is un-accelerated.
•  On the other hand, if a particle is un-accelerated, then we can surely say that the net forces acting on the particle is zero

Here, an important point to be noted that the first law does not distinguish between:

• The presence of the forces whose vector sum is zero and the absence of all the forces.
• A body moving with a uniform motion (i.e. with constant velocity) along a straight line and a body at rest.