Motion Under Gravity
Since, the value of ‘g’ does not depend upon the mass or distance of an object, therefore, all objects fall over the earth with the same rate. The equations for the motion are as follows:
Case-01: When the object is falling towards earth with an initial velocity (u), then
Velocity (v) after t seconds, v = u + gt
Height covered in t seconds, h = ut + ½gt2
Relation between v and u when t is not mentioned: v2 = u2 + 2gh
Case-02: When the object is falling from rest position means initial velocity u = 0 (zero), then
Velocity (v) after t seconds, v = gt
Height covered in t seconds, h = ½gt2
Relation between v and u when t is not mentioned: v2 = 2gh
Case-03: When the object is thrown vertically upwards with an initial velocity u, the gravitational acceleration will be negative (- g), then
Velocity (v) after t seconds, v = u - gt
Height covered in t seconds, h = ut - ½gt2
Relation between v and u when t is not mentioned: v2 = u2 - 2gh
In applying these equations, we will take acceleration, a to be positive when it is in the direction of the velocity, that is, in the direction of motion. The acceleration, a will be taken as negative when it opposes the motion.
