Free fall refers to the motion of an object under the influence of gravitational force only, with no other forces acting on it (like air resistance). When an object is in free fall, it accelerates downward due to gravity.

Equations of Motion for Free Fall

When an object falls freely from rest (initial velocity \( u = 0 \)), the equations of motion under gravity (\( a = g \)) are simplified versions of the standard kinematic equations.

1. When Initial Velocity \( u = 0 \):

First Equation of Motion:
\( v = g t \)
Second Equation of Motion:
\( s = \frac{1}{2} g t^2 \)
Third Equation of Motion:
\( v^2 = 2 g s \)

2. When Initial Velocity \( u \neq 0 \):

First Equation of Motion:
\( v = u + g t \)
Second Equation of Motion:
\( s = ut + \frac{1}{2} g t^2 \)
Third Equation of Motion:
\( v^2 = u^2 + 2 g s \)

Relationship Between Weight and Mass

Mass (\(m\)):

• Definition: Mass is a measure of the amount of matter in an object.
• Units: Kilograms (kg).
• Properties: Scalar quantity; intrinsic property of an object; does not change with location.

Weight (\(W\)):

• Definition: Weight is the force exerted on an object due to gravity.
• Formula: \( W = m \cdot g \)
• Units: Newtons (N).
• Properties: Vector quantity; depends on both mass and local gravitational field.

Example: Consider a 1 kg object:

• Mass: 1 kg (constant).
• Weight on Earth: \( 1 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 9.8 \, \text{N} \).
• Weight on the Moon: \( 1 \, \text{kg} \times 1.6 \, \text{m/s}^2 = 1.6 \, \text{N} \).