What are freely falling bodies? What is gravitational acceleration? Write down sign conventions for gravitational acceleration. Write three equations of motion of a freely falling body.

Freely Falling Bodies:

A freely falling body is an object that is falling under the influence of gravity only, without any resistance from air or other forces. This means that the only force acting on the body is the gravitational force, which pulls the object downward toward the Earth’s surface.

In real-world conditions, air resistance may slow the fall of a body, but in idealized conditions (such as in vacuum), freely falling bodies accelerate due to gravity alone. The acceleration is the same for all objects, regardless of their mass, assuming no air resistance.

Gravitational Acceleration:

Gravitational acceleration is the acceleration experienced by an object due to the force of gravity. Near the Earth’s surface, this acceleration is approximately 9.8 m/s². It means that the velocity of an object in free fall increases by 9.8 meters per second for each second it falls, assuming no other forces are acting on it (e.g., air resistance).

• The symbol for gravitational acceleration is g.
• The value of g is approximately 9.8 m/s² near Earth’s surface.

Sign Conventions for Gravitational Acceleration:

When solving problems involving freely falling bodies, sign conventions are essential for consistency in calculations. The standard sign convention for gravitational acceleration is as follows:

• Downward direction (towards the center of the Earth) is considered negative. Therefore, the acceleration due to gravity is taken as g = -9.8 m/s².
• Upward direction (opposite to the fall) is considered positive. If the object is thrown upwards, the acceleration due to gravity is still downward, so it remains negative.

Equations of Motion for a Freely Falling Body:

The three equations of motion describe the relationship between an object’s initial velocity, final velocity, acceleration, time, and displacement during its motion. For a freely falling body, the acceleration is -9.8 m/s² (due to gravity).

1. First Equation of Motion:

   v=u+at

   Where:

   • $v$ = final velocity
   • $u$ = initial velocity (which is 0 if the object starts from rest)
   • $a$ = acceleration (for free fall, this is -9.8 m/s²)
   • $t$ = time taken

2. Second Equation of Motion:

   s=ut+1/2at²

   Where:

   • $s$ = displacement (distance fallen)
   • $u$ = initial velocity (usually 0 if the object starts from rest)
   • $a$ = acceleration (for free fall, this is -9.8 m/s²)
   • $t$ = time taken

3. Third Equation of Motion:

   v²=u²+2as

   Where:

   • $v$ = final velocity
   • $u$ = initial velocity (usually 0 if the object starts from rest)
   • $a$ = acceleration (for free fall, this is -9.8 m/s²)
   • $s$ = displacement (distance fallen)

Example:

If a rock is dropped from rest (initial velocity = 0), after 2 seconds, its velocity will be:

Using the first equation of motion:

v=u+at=0+(−9.8)(2)=−19.6 m/s

This means the rock’s velocity after 2 seconds is 19.6 m/s downward.

Thus, these equations help us understand how objects behave when they fall freely due to gravity.