Difference between Gravitation Constant (G) and  Gravitational Acceleration (g)

Motion of Objects Under the Influence of Gravitational Force of the Earth

Let an object is falling towards earth with initial velocity u. Let its velocity, under the effect of gravitational acceleration g, changes to v after covering the height h in time t.

Then the three equations of motion can be represented as:
Velocity (v) after seconds, ght
Height covered in seconds, ut + ½gt2
Relation between v and u excluding tv2 = u2 + 2gh
The value of g is taken as positive in case of the object is moving towards earth and taken as negative in case of the object is thrown in opposite direction of the earth.