• 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. 