Free Fall Position Calculator

How to Use This Calculator

To calculate the position of an object in free fall, you need to know:

• The initial velocity (u) of the object
• The acceleration due to gravity (g)
• The time (t) of fall

Enter these values into the calculator and click "Calculate" to get the position of the object at any given time during its fall.

The Physics of Free Fall

When an object is in free fall, it is only subject to the force of gravity. Air resistance is negligible, and the acceleration is constant and equal to the acceleration due to gravity (g). On Earth, this value is approximately 9.81 m/s².

The equations of motion describe how the position, velocity, and acceleration of an object change over time. For free fall, we primarily use the equation for position as a function of time:

This equation shows that the position of the object increases quadratically with time, meaning the object falls faster and faster as time progresses.

Formula Explained

The free fall position formula is derived from the kinematic equations of motion. The key components are:

• Initial velocity (u): The velocity of the object at time t=0
• Acceleration due to gravity (g): Approximately 9.81 m/s² on Earth
• Time (t): The duration of the fall

The formula accounts for both the initial velocity component (ut) and the acceleration component (½gt²) that causes the object to fall faster over time.

Worked Example

Let's calculate the position of a rock dropped from a cliff with an initial velocity of 0 m/s after 3 seconds.