Equations of Motion Under Gravity

Introduction

When an object moves under the influence of gravity alone, its motion is called motion under gravity. In such motion, the acceleration is constant and is equal to the acceleration due to gravity (g).

These motions are explained using the standard equations of motion by replacing acceleration (a) with g.

Definition

Equations of motion under gravity are the mathematical relations that describe the motion of a body when it is moving vertically under the influence of gravitational force.

Explanation

Near the surface of the Earth, every freely falling body experiences a constant acceleration called acceleration due to gravity (g ≈ 9.8 m/s²).

By replacing acceleration (a) with g in the equations of motion, we get:

v = u + gt

s = ut + (1/2)gt²

v² = u² + 2gs

Where:

u = initial velocity
v = final velocity
s = displacement
t = time
g = acceleration due to gravity

Sign Convention

The direction of motion is very important while solving problems:

If the body is moving downward (free fall), g is taken as positive.
If the body is thrown upward, g is taken as negative.

In simple terms:

Upward motion → velocity decreases → g is negative
Downward motion → velocity increases → g is positive

Types

1. Body Falling Downward

Initial velocity (u) = 0 (if dropped)
g is positive
Velocity increases with time

2. Body Thrown Upward

Initial velocity (u) is upward
g is negative
Velocity decreases until it becomes zero at highest point

3. Highest Point

Final velocity (v) = 0
Acceleration is still g downward

Importance

Used to calculate height, time, and velocity of falling objects
Helps in understanding motion of projectiles
Important in solving numerical problems in physics

Examples

A stone falling from a building
A ball thrown upward and coming back down
Rain falling from clouds

An important point:

All bodies fall with the same acceleration (g) regardless of their mass (ignoring air resistance)

Important Points

Acceleration due to gravity (g) is constant near Earth surface
For downward motion, g is taken as positive
For upward motion, g is taken as negative
At highest point, velocity becomes zero
Time of ascent equals time of descent (for same height)
All bodies fall with same acceleration (independent of mass)
Choose correct equation based on known values

Conclusion

Equations of motion under gravity help us understand and calculate the motion of objects moving vertically under Earth's gravitational force. By applying proper sign conventions and formulas, we can easily solve various real-life and numerical problems.

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