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The acceleration due to gravity, often represented by the symbol \( g \), is the rate at which an object accelerates when it is falling freely toward Earth. On our planet, this value is approximately \( 9.8 \text{ m/s}^2 \). This means that every second, the velocity of a freely falling object increases by \( 9.8 \text{ m/s} \).
When calculating problems involving objects under free fall, we generally assume that air resistance is negligible. This simplifies our calculations and allows us to rely on the constant value of gravity. This concept is crucial in understanding the motion of objects not only on Earth but also helps in studying celestial bodies. Many physics problems start by identifying this constant to predict how objects move under the influence of gravity.

Free fall is a special kind of motion that occurs when only gravity is acting on an object. When an object is in free fall, it does not encounter air resistance or external forces.

• The only force acting on it is the gravitational pull.
• Its initial velocity is zero if you simply let go of it.
• It accelerates continuously at the rate of gravity \( g \), which is \( 9.8 \text{ m/s}^2 \) on Earth.

Understanding the principles of free fall is essential in physics because it provides a basis for analyzing more complex motions when other forces come into play.

To analyze the motion of objects, such as a marble being dropped from a great height, we utilize motion equations, specifically the kinematic equations. These help us describe motion mathematically without needing to delve into the reasons behind it.
One key equation is used to determine the time it takes an object to reach the ground, and another is used to find its final velocity just before impact. Here's how they both look:

• To find time \( t \), we use \( h = \frac{1}{2}gt^2 \). Solving for \( t \) gives us the time it takes for a free-falling object to hit the ground from a known height \( h \).
• To find the final velocity \( v \) just before it hits the ground, we use \( v = gt \).

The simplicity of these equations allows us to solve complex motion problems with minimal input data. By measuring the height and using the constant acceleration due to gravity, predicting the outcome of a free fall experiment becomes straightforward.