Table of Contents
Fall Distance Basics
The distance an object falls increases quadratically with time because velocity increases linearly. In the first second, an object falls 4.9 m. In the second, it falls an additional 14.7 m (total 19.6 m). By the third second, the total is 44.1 m. This accelerating nature of free fall makes even short falls potentially dangerous.
The quadratic relationship (d proportional to t^2) was first demonstrated by Galileo, who rolled balls down inclined planes to slow the motion enough for measurement. This discovery was revolutionary, overturning the Aristotelian view that heavier objects fall proportionally faster.
Formula
For an object starting from rest (v0=0): d = 1/2 * g * t^2 = 4.905 * t^2 meters.
Distance Table
| Time (s) | Distance (m) | Speed (m/s) |
|---|---|---|
| 1 | 4.9 | 9.8 |
| 2 | 19.6 | 19.6 |
| 3 | 44.1 | 29.4 |
| 5 | 122.6 | 49.1 |
| 10 | 490.5 | 98.1 |
FAQ
Why does distance increase quadratically?
Velocity increases linearly (v = gt), and distance is the integral of velocity over time. Integrating a linear function gives a quadratic: d = 1/2*g*t^2. Each successive second, the object covers more distance because it is moving faster.
How far is a 1-second fall?
About 4.9 meters (16 feet). This is roughly the height of a one-story building. The impact speed is 9.8 m/s (35 km/h or 22 mph), which can cause serious injury.
Does mass affect fall distance?
In vacuum, no. All objects fall the same distance in the same time regardless of mass. In air, denser objects fall slightly farther in a given time because they are less affected by air resistance. But for most practical purposes near Earth's surface, the difference is negligible for solid objects.