Why don't electrons fall or collapse around atom when an object accelerates rapidly? In laws of motion, everything has an equal and opposite reaction, and it applies to all matters in the reality.
If the earth stops moving suddenly just for one second, then everything on earth will be thrown out into space. But sudden rapid movement or sudden stop of motion does not cause the electrons to lose control around the nucleus or atom. Why? (For example: putting the brakes on suddenly in a car while traveling around the speed of $180$ km/h, creates massive momentum transfer and that momentum does not affect the electron's path of the car or the person sitting inside the car?) Is it because of the strength of the attraction between electron and nucleus?
NOTE: Thanks for the edit and I understand the transfer of momentum energy is transferred to the whole system, not just some part but still the momentum is high for an electron when 180 km/h suddenly stops, The whole atomic field will receive the massive vibrations caused by momentum and still the path of the electron is not disturbed in atomic level ? and is that because of the attraction between electrons and the nucleus?
 A: At first, as others have said,- you transfer car momentum to a whole atom system, not just to some part of it,- like electrons, nucleus, etc.
Second,- an electron is not something you can easily mess around. If you look at the semi-classical Bohr atom model, an electron goes with a tangential speed around the nucleus defined by:
$$ v={\sqrt {\frac {Zk_{\mathrm {e} }e^{2}}{m_{\mathrm {e} }r}}}. $$
So for example the electron in a hydrogen atom at the ground level flies with amazing
$\approx 2000 ~\text{km/s}$ speed. That's about $1\%$ of light-speed! If converted to an electron centripetal acceleration notion, gives about $10^{21}\text {g}$. Thus an atom's electrodynamical system is a very stable thing.
That said, you can push an electron out of an atom. But for doing that you need some different approach, like scattering the hydrogen nucleus with high-speed neutrons in a particle accelerator or just "stretching" a hydrogen atom in a static electric field, so that it would overcome an ionization energy of $13~\text {eV}$, or forcing a hydrogen atom to absorb such an energy photon.
A: The laws of motion you are quoting are the classical Newtonian mechanics  laws. They do not hold as such at the quantum level, they are emergent for energies and distances where classical mechanics applies.
In your specific example the entity is the atom, a quantum mechanical bound state. The electrons are not separate from the nucleus as far as classical kinematics goes.The whole atom accelerates, not its individual components.
A: There is a nice answer by @annav, I would like to give an example where a certain type of acceleration could in theory tear apart the atom. As you can see from the other answers, the atom is usually (in terms of acceleration) regarded as a quantum mechanical whole entity, and accelerates as a whole (like in your example).
Now here is the catch. The answer depends on the type (and form) of acceleration, that is, whether you are assuming in your example the same level of acceleration for the whole atom as an entity. That being said, the strong and EM forces holding the atom together are really "strong".

Anything above elementary particles should in theory be ripped apart, yes.

Spaghettification on an atomic scale?
But not infinitely strong. It is being theoretically suggested, that inside a black hole, the tidal forces could be stronger then the forces binding the atom, and in theory, the atom could be torn apart by the tidal effects of gravity. Why? Because the acceleration changes so rapidly, that different "parts" of the atom could undergo different levels of acceleration, and this, if the difference reaches a certain level, could overcome the binding forces, resulting in a torn atom.
A: 
But sudden rapid movement or sudden stop of motion does not cause the electrons to lose control around the nucleus or atom.

Sudden stop of motion is not something that occurs in nature but as a whole what you are describing is a collision event. Depending on the energies involved such collisions do have the potential to eject electrons from atoms.
For example, at very high temperatures, thermal collisions may create a plasma of ions and free electrons.
In the case of the collision you are describing with speeds in the range of
180 km/h the energy is much to small to eject electrons and ionize matter.
To achieve that you would have to up the speed to the range of tens of km/s. Think of a meteorite hitting the atmosphere or ground.
In the case you are describing, the kinetic energy is converted into thermal energy and part of the thermal energy is converted into electromagnetic radiation (mainly in the infrared spectrum)
Like others have commented above, the view that electrons are small particles whizzing around the atomic nucleus on rigid orbits like planets around a star is totally outdated. Bohr and Rydberg presented it over hundred years ago. It was clear then that it can't be quite right since electrons should radiate energy when orbiting the nucleus.  We know that all charged particles radiate energy when accelerated.
Our current understanding is that electrons bound to an atom exists in steady states each being described by a quantum mechanical wave function. Each electron state has a certain binding energy. However, these states can be influenced by external fields and thermal collisions creating non-uniform time-dependent charge distributions that radiate electromagnetic energy. As you are reading this your body radiates electromagnetic energy at an average rate of 100W.
A: An acceleration of order $g\approx 10$ m/s$^2$ is utterly negligible compared to the acceleration of an electron in an atom.
A: Some of the answers are implying that the answer lies within the quantum effects of the electron, but there's a pretty intuitive answer if you think of the system as classical -- and I suspect the quantum answer is just a slight modification of this.
If you could pull the nucleus of an atom on a string, there will be some speed where if you tug it too hard the electron will get left behind.
Comparing to your example: A car suddenly stopping will cause a person to fly into the windshield. But a car that doesn't stop as sudden will not cause a person to have any issues. This is because the friction between the person and the car keeps them in equilibirum dispite the additional inertial force.
Another example: If the was sun moved slowly enough, the planets would still follow it in orbit. But if the sun was jerked away too quickly, many or all of the planets could get left behind.
