Understanding the Concepts

* Free Fall: An object in free fall experiences only the force of gravity.

* Acceleration due to Gravity (g): The constant acceleration experienced by objects in free fall. On Earth, it's approximately 9.8 m/s².

* Kinematic Equations: We'll use a kinematic equation to relate the distance, time, and acceleration.

The Equation

The most suitable kinematic equation for this problem is:

* d = v₀t + (1/2)gt²

Where:

* d = distance (3.0 meters)

* v₀ = initial velocity (0 m/s since it's released from rest)

* t = time (1.0 second)

* g = acceleration due to gravity (what we want to find)

Solving for g

1. Plug in the values:

3.0 m = (0 m/s)(1.0 s) + (1/2)g(1.0 s)²

2. Simplify:

3.0 m = (1/2)g(1.0 s)²

3. Solve for g:

g = (3.0 m) / [(1/2)(1.0 s)²]

g = 6.0 m/s²

Answer:

The magnitude of the acceleration due to gravity on this planet is 6.0 m/s².