Avolume of cool air rapidly descends from the top of a mountain. the air is a poor thermal conductor, but its temperature increases as its volume decreases, because of the increase in atmospheric pressure as it reaches the ground. what thermodynamic process takes place

These are all the characteristics of what is called the adiabatic process. This process occurs when there is no transfer of heat between the surroundings and the thermodynamic system. This is a key process for thermodynamics and it is of great importance for the first law of thermodynamics. 

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.