Study Notes on Free Fall Motion and Calculations

Introduction to Motion in Free Fall

This study guide covers the fundamental concepts of motion in free fall, addressing key equations, calculations, and physical interpretations of falling objects in the context of gravity.

Motion of Objects under Gravity

Free Fall

Objects in free fall are influenced solely by the force of gravity, causing them to accelerate downwards at approximately 9.81 \text{ m/s}^2. This acceleration is referred to as the acceleration due to gravity, denoted by the variable g.

Initial Conditions

Assume a rock is initially at rest before being dropped. Therefore, its starting velocity, represented by v0, is: v0 = 0 \text{ m/s}\

When the rock is released from a height, we are interested in determining how far it falls after a specific duration, such as 3 seconds.

Key Concepts

Variables

• Acceleration (a): The acceleration of the rock due to gravity is constant, a = 9.81 \text{ m/s}^2.
• Initial Velocity (v0): For the rock at rest, the initial velocity is v0 = 0 \text{ m/s}.
• Time (t): The time duration of the fall, in our case, is 3 seconds.
• Displacement (d): The vertical distance the rock falls, which we want to calculate.

Equations of Motion

To calculate the displacement of the rock while it falls, we use the second equation of motion:

d = v_0 t + \frac{1}{2} a t^2\

Substituting in our known values:

• v_0 = 0 (since it starts from rest)
• a = 9.81 \text{ m/s}^2
• t = 3 \text{ s}

The equation simplifies to:

d = 0 \cdot 3 + \frac{1}{2} (9.81) (3^2)

Solving further:
= \frac{1}{2} (9.81) (9)
= \frac{1}{2} (88.29)
= 44.145 \text{ m}

Thus, after 3 seconds, the rock falls a distance of approximately 44.15 meters. The final calculated distance can vary slightly based on rounding of the gravitational acceleration value.