#### Introduction

An object’s acceleration is the rate at which its velocity changes over time. The acceleration of an object is the result of all the forces acting on it, according to Newton’s second law. Gravity is the only force acting on a freely falling object under ideal circumstances. Calculate the displacement of an object that is free falling, calculate its average velocity at set intervals, and calculate its acceleration due to gravity.

#### Theory

When do we get to know if there is acceleration or not?

- Drop something you pick up with your hand. As soon as you release it from your hand, its speed is zero. As it descends, its speed increases. As it falls, it travels faster. To me, that sounds like acceleration.
- Acceleration is not just about increasing speed. Toss this same object vertically into the air. On the way up, its speed decreases until it stops and reverses direction. Acceleration also refers to a decrease in speed.
- Acceleration involves more than just changing speed. One last time, launch your battered object. Throw it horizontally this time, and observe how its horizontal velocity gradually becomes vertical. Considering that acceleration is the rate at which velocity changes with time and velocity is a vector quantity, this change in direction is also considered acceleration.

Gravity was pulling the object down, so it was accelerating. The moment an object leaves your hand, it begins to fall – even if thrown straight up. In the absence of this, it would have continued moving away from you in a straight line. Gravity causes this acceleration.

Gravitational acceleration varies slightly with latitude and height above the earth’s surface. Sea level is experiencing greater acceleration due to gravity than Mount Everest at sea level and the poles are experiencing greater acceleration due to gravity at the equator. Free falling objects do not encounter a significant amount of air resistance; they fall solely under the influence of gravity. No matter how heavy an object is, it will fall with the same rate of acceleration. Galileo demonstrated with a demonstration that mass doesn’t really matter when it comes to free falling, contrary to what was previously thought.

#### Famous leaning tower of Pisa demonstration

This phenomenon was also observed by Galileo, who recognized that it was contrary to Aristotle’s principle that heavier items fall more quickly. According to an apocryphal tale, Galileo (or an assistant, more likely) dropped two objects of unequal mass from the Leaning Tower of Pisa. Contrary to Aristotle’s teachings, both objects struck the ground simultaneously (or very nearly so). Galileo probably couldn’t have obtained much information from this experiment given the speed at which the fall would occur. The majority of his observations of falling bodies were of round objects rolling down ramps. Water clocks and his own pulse were used to measure the time intervals (stopwatches and photogates hadn’t yet been invented). Until he reached an accuracy of one tenth of a pulse beat between two observations, he repeated this “a hundred times.”

The instant when the balls are released is considered to be the initial time t = 0. The position of the ball along the ruler is described by the variable y. The position of the ball at a time t is given by

\(\large y(t)=y_0{}+v_0t+\frac{1}{2}g t^{2}\).

If the ball is released from rest, the initial velocity is zero: v0 = 0. Therefore,

\(\large y(t)=y_0+\frac{1}{2}g t^{2}\).

Free fall bodies accelerate at -9.8 m/s (negative sign indicates downward acceleration). However, the acceleration of

A free falling body has a velocity of -9.8 m/s in the kinematic equation.

2) A drop from a particular height has an initial velocity of 0 m/s.

When an object is projected upwards vertically, it will slowly rise up. When it reaches 0 m/s, its velocity is zero

The apex of its trajectory.

#### Question:

Calculate the body height if it has a mass of 1 kg and after 9 seconds it reaches the ground?

#### Answer:

Given: Height h =?

Time t = 9s

We all are acquainted with the fact that free fall is independent of mass.

Hence, it is given as

\(\large h=\frac{1}{2}g t^{2}\).

h=0.5 * 9.8 * (9)^{2}

h= 396.9

#### Falling with Air Resistance

It is common for an object to encounter some degree of air resistance as it falls through the air. Air molecules collide with the object’s leading surface, causing air resistance. There are a variety of factors that determine how much air resistance the object encounters. The speed of the object and its cross-sectional area are two factors that have a direct effect upon the amount of air resistance. An increase in speed results in an increase in air resistance. The amount of air resistance increases with an increase in cross-sectional area.

#### Common mistakes and misconceptions

A falling object’s final velocity is mistakenly assumed to be zero once it hits the ground. It is the speed just before touching the ground that determines the final velocity in physics problems. As soon as the object touches the ground, it ceases to be in freefall.

#### Math Coding

```
fun height(gravity: Double, seconds: Double): Double {
return 0.5 * gravity * Math.pow(seconds, 2.0)
}
fun velocity(gravity: Double, seconds: Double): Double {
return gravity * seconds
}
fun time(velocity: Double, gravity: Double): Double {
return velocity / gravity
}
//Execution for Test Purpose
val gravity = 9.80665
var time = 10.0
val height = height(gravity, time)
val velocity = velocity(gravity, time)
time = time(velocity, gravity)
println("$velocity m/s")
println("$time seconds")
println("$height meter")
```

#### Output

```
98.06649999999999 m/s
10.0 seconds
490.3325 meter
```

#### Conclusion

A free-falling object is studied using the kinematic equations. As a free falling object falls, it will be influenced by gravity. A free falling object has two main characteristics: it does not encounter air resistance, and it accelerates at a rate of 9.8 m/2. We can determine the height, velocity and time of free fall using the formula.

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