Conservation Principle We are introduced to Principle of Conservation of Linear Momentum via the Newton's Second Law
$$\vec{F_{net}}=\frac{d\vec{p}}{dt}$$
It states when net external force equals zero then $\vec{p}=$constant. Hence we say linear momentum to be conserved.
Although I know that there are no proofs of conservation laws and they can only be verified just like here it simply means it is consistent with the second law of motion.
My query may look meaningless but still as they say, "The only “dumb” question is the one that is not asked."
Can we in a similar manner present by saying:

*

*When there is no net acceleration$\;(\vec{a}\;$) then velocity $\;(\vec{v})\;$ is constant or conserved.
$$\vec{a}=\frac{d\vec{v}}{dt}$$

*When there is no velocity $\;(\vec{v}\;$) then displacement $\;(\vec{r})\;$ is constant or conserved.
$$\vec{v}=\frac{d\vec{r}}{dt}$$
As it is clear that comment 1 is consistent with First Law of Motion and certainly the comment 2 as well.
But one may argue that these results ain't meaningful from the context of Mechanics.
Linear Momentum is the quantity of motion contained in the body.
Or these cannot be added to set of conservation laws as their idea is already presented
by kinematical equations and laws of motion.
Why don't we consider them into conservation laws?
 A: 
Although I know that there are no proofs of conservation laws and they can only be verified just like here it simply means it is consistent with the second law of motion.

On the contrary, probably the most elegant and influential proof of all physics is Noether's theorem which proves that conservation laws are associated with symmetries of the action. In a nutshell, Noether's theorem says that for every differential symmetry of the action (in other words a small change that you can make to the state of the system that does not change the action) there is a conserved quantity.
In particular, the laws of physics are the same from place to place. So if you move your system to the left a little then the action will be the same. This symmetry is called spatial translation symmetry, and it is this symmetry that leads to the conservation of momentum.
As an example, consider the Lagrangian of a free particle $$\mathcal{L} = \frac{1}{2}m \dot x^2$$ this Lagrangian does not depend on $x$, which leads to a conserved momentum $$p=\frac{\partial \mathcal{L}}{\partial \dot x} = m \dot x$$

When there is no net acceleration(a⃗ ) then velocity (v⃗ ) is constant or conserved.

There may be some possible Lagrangian that would have a symmetry that would lead to conservation of acceleration, but I am not sure what that would be and I don't think it would represent the Lagrangian of any real physical system.

When there is no velocity (v⃗ ) then displacement (r⃗ ) is constant or conserved.

Same as for acceleration.
