Free Fall

1. Definition

Free fall is the motion of an object under the influence of gravity only, with all other forces (such as air resistance) neglected.

2. Acceleration Due to Gravity

Near the surface of Earth, all objects in free fall experience a constant acceleration:

\(\vec{a}=\vec{g}\)​

Magnitude:

\(g=\approx{9.8}m/s^2\)

Direction:

• always toward the center of the Earth (downward)

3. Sign Convention

To solve problems, you must choose a coordinate system.

Common choice:

• upward → positive
• downward → negative

Then:

\(a=-g=-9.8m/s^2\)

4. Kinematic Equations for Free Fall

Since acceleration is constant, the Big Five equations apply.

Velocity

\(v=v_0+at\)

Position

\(y=y_0+v_0t+\frac{1}{2}at^2\)

Velocity–Position

\(v^2={v_0}^2+2a(y-y_0)\)

5. Special Cases

(1) Dropped Object

Initial velocity:

\(v_0=0\)

Then:

\(v=gt\)

\(y-y_0=\frac{1}{2}gt^2\)

(direction depends on sign convention)

(2) Thrown Upward

• initial velocity upward
• acceleration downward

Key points:

• velocity decreases as it rises
• at the highest point : v=0

• then it accelerates downward

(3) Falling Downward

If thrown downward:

• initial velocity and acceleration are in the same direction
• speed increases continuously

6. Time Symmetry (No Air Resistance)

In ideal free fall:

• time going up = time coming down
• speed at a given height is the same going up and down

This follows from constant acceleration.

7. Graphical Interpretation

Velocity–Time Graph

• straight line with slope −g (if upward is positive)

Position–Time Graph

• parabola (curved path)

8. Physical Meaning

Free fall demonstrates that:

• all objects accelerate at the same rate (ignoring air resistance)
• motion under gravity is uniformly accelerated motion
• gravitational acceleration determines how velocity and position change

Summary

Free fall is motion under gravity alone.

\(a=g\approx9.8m/s^2\)

Kinematic equations apply:

\(v=v_0+at\)

\(y=y_0+v_0t+\frac{1}{2}at^2\)

\(v^2={v_0}^2+2a(y-y_0)\)

Key ideas:

• acceleration is constant and downward
• motion is symmetric (without air resistance)
• applies to objects dropped, thrown up, or thrown down