Free Fall
Free fall is the motion of an object under the influence of gravity alone, with no other forces such as air resistance acting on it. Near Earth's surface, all freely falling objects experience the same constant downward acceleration g ≈ 9.8 m/s², regardless of their mass — a result first demonstrated experimentally by Galileo Galilei. Free fall is a special case of uniformly accelerated motion.
Key Formula
v = u + g×t and h = u×t + ½×g×t²
LaTeX: v = u + gt \quad \text{and} \quad h = ut + \frac{1}{2}g t^2
| Symbol | Meaning | Unit |
|---|---|---|
| v | Velocity at time t | m/s |
| u | Initial velocity (0 if dropped from rest) | m/s |
| g | Acceleration due to gravity (≈ 9.8 m/s²) | m/s² |
| t | Time elapsed | s |
| h | Vertical distance fallen | m |
Worked Example
Problem
A stone is dropped from rest off a cliff. How far does it fall in 3 seconds, and what is its velocity just before hitting the ground? (Take g = 9.8 m/s², ignore air resistance.)
Solution
Step 1: Initial velocity u = 0 (dropped from rest). Step 2: Distance: h = ut + ½gt² = 0×3 + ½×9.8×3² = 0 + ½×9.8×9 = 44.1 m. Step 3: Final velocity: v = u + gt = 0 + 9.8×3 = 29.4 m/s.
Answer
Distance fallen = 44.1 m; Velocity at impact = 29.4 m/s downward.
Free-fall velocity and distance at successive seconds (dropped from rest, g = 9.8 m/s²)
| Time (s) | Velocity (m/s) | Distance fallen (m) | Notes |
|---|---|---|---|
| 0 | 0 | 0 | Moment of release |
| 1 | 9.8 | 4.9 | After 1 second |
| 2 | 19.6 | 19.6 | After 2 seconds |
| 3 | 29.4 | 44.1 | After 3 seconds |
| 4 | 39.2 | 78.4 | After 4 seconds |
| 5 | 49.0 | 122.5 | After 5 seconds |
Interactive Tools
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Related Terms
Acceleration
Acceleration is the rate of change of velocity with respect to time, and is a vector quantity. An object accelerates whenever its speed changes, its direction changes, or both simultaneously. Acceleration is caused by a net force (Newton's second law) and is measured in metres per second squared (m/s²).
Projectile Motion
Projectile motion is the two-dimensional motion of an object launched into the air that moves under the influence of gravity alone, following a curved (parabolic) trajectory. The horizontal and vertical components of motion are independent: the horizontal component is uniform (constant velocity), while the vertical component is uniformly accelerated by gravity (g ≈ 9.8 m/s²). Galileo first described this decomposition in the early 17th century.
Velocity
Velocity is the rate of change of displacement with respect to time, making it a vector quantity with both magnitude (speed) and direction. Average velocity equals total displacement divided by total time, while instantaneous velocity is the derivative of position with respect to time. Velocity is central to Newton's laws and is measured in metres per second (m/s).
From Old English "feallan" (to fall) combined with "free". The scientific term gained precision through Galileo's 16th-century experiments at the Leaning Tower of Pisa, demonstrating mass-independent gravitational acceleration.