Motion of objects under the influence of the gravitational force of the earth:

Let us see activity to understand whether all the objects reach the surface at the same time when it falls from the same height.
Step 1:

Take an A4 sheet of paper and a small stone.
Step 2:

Drop them simultaneously from a certain height.
Step 3:

Check which one reaches the ground first?
The stone will reach the ground first, and then the paper will reach the ground.
So, do you think the force acting on the objects vary from one to another?

No. The acceleration due to gravity is constant for all the objects near the earth surface. The reason for the late arrival of paper is due to the air resistance. Since the paper is lighter in weight and covers a large area in space compared to the stone, the air offers more resistance to the paper than the stone. Thus, the stone reaches the ground quickly.
We know that an object experiences acceleration when it falls freely under gravity. The acceleration experienced by an object is independent of its mass. No matter how big or small, hollow or solid, all the object should fall at the same rate. Galileo dropped different objects from the top of the Leaning Tower of Pisa to prove the same. As \(g\) is fixed near the earth, all the equations for the uniformly accelerated motion of objects become true, with acceleration replaced by \(g\).
u - initial velocity
v - final velocity
t - time taken
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.