Can the law of the acceleration be applicable to a man falling from plane? Is acceleration law
$a = \Delta v/\Delta t$
applicable on somebody who is falling from an air plane? Does the acceleration increase when some body is at some altitude and does his speed increases by  $9.81 m/s$   every second (because of the gravity of the average earth) ?
 A: If I understand what you asked, yes that is the situation for which acceleration due to gravity is applied.
However, there is a terminal velocity due to air resistance, and the Acceleration and resistance will reach equilibrium. The wikipedia page discusses skydiving first, and that is what the activity of purposefully jumping out of a plane is called.
A: Yes speed will increase $9.8$ m/s every second provided that there is no other force acting as resistance to the fall.
In reality air resistance depends on speed and the faster someone falls the more the resistance of the air around them. Eventually any object falling through the atmosphere will reach 'terminal velocity' the speed at which the force downwards of gravity is balanced exactly by a force upwards of wind resistance. 
One final point is that at high altitude the acceleration due to gravity will be slightly less as the acceleration due to gravity depends on the distance from the centre of the earth. - but then the air is less dense so the air resistance will be lower and the terminal veocity will be higher.
