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How does the velocity of an object change during a free fall,derive the expression for 'g'when the object is near the surface of earth
An object  is dropped near the surface of the earth it experiences an acceleration of 9.8 meters per second . This means that for every second that an object falls, it increases its speed by 9.8 meters per second. An object dropped from rest will fall 9.8 m/s, after the 1st second, about 19.6 m/s after the 2nd second, about 29.4 m/s after the 3rd and so on. 
1.The  position versus time graph for a free-falling object is shown  as :



2.The velocity versus time graph for a free-falling object is shown as



Expression for gravitational constant :



The equation for the force due to  gravity is equal to 



The force on an object of mass m1 near the surface of the Earth is :
f = m1g

This force is due to gravity between the object and the Earth, according to Newton’s y formula, 




The radius of the Earth, re =  6.38 × 106 m, 
The  mass of the Earth, m =  5.98 × 1024 kg

Substituting the values , we get





ie , 


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