How force affect the objects that we apply on? Why do things get accelerated rather than do a moving at constant speed when we apply a force on them? How my force affect the object at atomic level? Does it increase the kinetic energy of atoms ? If it does, why ı can't observe the same event when ı heat them(cus both of these increase the kinetic energy)?
 A: 
Why do things get accelerated rather than do a moving at constant
  speed when we apply a force on them?

They accelerate if there is a net force applied to them per Newton's second law, $F_{net}=ma$. Things remain stationary or move with constant velocity when there is either no force applied, or if the net force applied is zero, per Newton's first law.

How my force affect the object at atomic level? Does it increase the
  kinetic energy of atoms ? If it does, why ı can't observe the same
  event when ı heat them(cus both of these increase the kinetic energy)?

Objects have internal energy, the microscopic kinetic and potential energies of the atoms and molecules of the object. Your force can have an effect on those energies. For example, if the force causes an object to deform at the same time as it causes it to accelerate, it can increase the microscopic kinetic energies of the atoms due to internal friction. You can't "see" the increase in the microscopic kinetic energy but you might be able to measure an increase in temperature of the object because of the increase in kinetic energy. 
You can also increase the internal microscopic kinetic energy of the atoms an molecules by means of heating the object, i.e., exposing the object to something else at a higher temperature. Of course increasing the kinetic energy by means of heat does not cause the object as a whole to accelerate, as when you apply a force.
Hope this helps.
