The first law of motion, also called Law of Inertia, is:
An object in motion or at rest tend to stay in rest or motion unless acted on by an unbalanced force.
“An object in motion will stay in motion and an object at rest will stay at rest unless and until acted upon by an external unbalanced force”
Imagine an object in empty space. It it is not moving, it will not begin to more unless an unbalanced force acts on it. This itself is intuitive. Less so, is the other aspect. Again imagine an object in empty space, but this time with a velocity. This object will continue to move with the velocity unless an unbalanced force acts on it.
There are two equal statements of this law.
First:
Force is equal to mass times acceleration, $F_\text{net} = ma$
Second:
Momentum is equal to mass into velocity, $p = mv$
Force is directly proportional to mass and acceleration and momentum is directly proportional to mass and velocity. But how do these two ideas relate?
$$ F=ma\newline F=m\frac{v-u}t\newline F=\frac{mv-mu}t\newline F=\frac{p_{\text{f}}-p_{\text{i}}}t\text{, momentum formula}\newline F=\frac{\Delta p}t $$
Force is the rate of change of momentum.
Momentum can be defined as “mass in motion”. It is vector quantity, the direction component coming from the velocity. It is measured in kilogram meter per second, $kgms^{-1}$.
In an isolated system, the momentum before and after an event must, necessarily, be equal. (The final and initial momentum in a closed system are equal)