Yes, it is entirely possible to travel a great distance and yet have zero displacement.
Understanding Distance vs. Displacement
To grasp this concept, it's crucial to understand the fundamental difference between distance and displacement in physics:
- Distance: This is a scalar quantity that measures the total length of the path an object has traveled, regardless of direction. It's the odometer reading in a car, representing the total ground covered. Distance is always a positive value or zero.
- Displacement: This is a vector quantity that measures the shortest straight-line path from an object's initial position to its final position, including the direction. It indicates how far an object is from its starting point and in what direction. Displacement can be positive, negative, or zero.
The key distinction lies in the fact that distance tracks the entire journey, while displacement only cares about the starting and ending points.
Key Differences at a Glance
For a clearer comparison, consider the following table:
| Feature | Distance | Displacement |
|---|---|---|
| Type | Scalar quantity | Vector quantity |
| Measures | Total path length covered | Change in position |
| Depends On | The specific path taken | Only initial and final positions |
| Can Be | Always positive or zero | Positive, negative, or zero |
| Direction | Not considered | Crucial for its definition |
Examples of Great Distance with Zero Displacement
The possibility of traveling a significant distance with no displacement occurs when an object returns to its original starting point. Even if it covers many miles or kilometers along the way, if its final position is identical to its initial position, its net change in position (displacement) is zero.
Here are several practical examples:
- Automobile Races: A car competing in a race on a circular or oval track, like a NASCAR circuit, covers hundreds of miles. However, once it crosses the finish line, returning to its starting point, its displacement for that complete lap or race is zero.
- A Round Trip: If you drive from one city to another and then return to your original city, you have covered a substantial total distance. Yet, because your journey began and ended at the same location, your overall displacement is zero.
- Earth's Revolution: The Earth travels an immense distance as it revolves around the Sun. After one complete revolution (approximately 365 days), it returns to roughly the same point in its orbit relative to the Sun. Over that year, the Earth's displacement relative to its position a year prior is effectively zero, despite traveling millions of miles.
- Walking Around a Block: If you leave your house, walk around the entire city block, and return to your front door, you've certainly walked a distance. However, since your final position is the same as your starting position, your displacement is zero.
- Pendulum Swing: A pendulum bob travels a distance as it swings back and forth. If you consider its motion from one extreme point back to the same extreme point, it covers a distance, but its displacement for that full swing is zero.
Practical Insights
This concept is fundamental in physics and engineering, especially in fields like navigation, robotics, and aerospace. While distance is crucial for calculating fuel consumption, tire wear, or physical effort, displacement is vital for determining an object's final position relative to its origin, understanding net movement, or calculating average velocity (which depends on displacement, not distance). A GPS system might show you a path you've traveled (distance), but it also accurately pinpoints your location, highlighting when you've returned to your starting point (zero displacement).
