The acceleration of a free-falling object is dictated by the gravitational force acting on it, which is typically approximately $9.81 \, \text{m/s}^2$ on Earth.

When an object is in free fall, the sole force acting upon it is gravity, which pulls the object toward the center of the Earth or any other celestial body, depending on its location. The acceleration due to gravity on Earth is around $9.81 \, \text{m/s}^2$. This indicates that for each second an object is in free fall, its velocity increases by about $9.81 \, \text{m/s}$ in the downward direction. To fully grasp this concept, one might consider how acceleration is defined and measured within the broader context of motion in physics.

It’s important to note that the gravitational acceleration can vary slightly based on geographical location due to factors such as altitude and the Earth’s rotation. For instance, the acceleration due to gravity is marginally lower at the equator compared to the poles. However, for most practical purposes, especially at the high school level, we commonly use the standard value of $9.81 \, \text{m/s}^2$. Understanding the concept of acceleration in physics is essential for accurately interpreting these measurements.

To calculate the acceleration of a free-falling object, one must measure the change in velocity over a specific time interval. This can be accomplished through various methods, such as using a stopwatch to measure the distance fallen or employing more advanced equipment like a motion sensor. Once these values are obtained, acceleration can be calculated using the formula:

$a = \frac{\Delta v}{\Delta t}$

where $a$ represents acceleration, $\Delta v$ denotes the change in velocity, and $\Delta t$ signifies the change in time. This process illustrates a practical application of acceleration in observing objects in motion under the influence of gravitational forces.

It is crucial to understand that this acceleration remains constant for a free-falling object, irrespective of its mass. This principle, first identified by Galileo and later integrated into Newton’s law of universal gravitation, implies that whether you drop a feather or a hammer, both will accelerate toward the Earth at the same rate in the absence of air resistance. This concept can be somewhat counterintuitive, but it is a fundamental aspect of our understanding of gravity and motion. Additionally, exploring the relationship between mass and velocity can deepen our comprehension of how these factors interact during free fall.