Differences between distance and displacement:
| Aspect | Distance | Displacement |
|---|---|---|
| Definition | The total length of the path traveled by an object is called distance ( direction is not considered). | The shortest straight-line distance between the initial and final positions of an object is called displacement (along the initial to final direction). |
| Nature | Scalar quantity (it has only magnitude). | Vector quantity (it has both the magnitude and direction). |
| Tensor | Tensor of rank-0 | Tensor of rank-1 |
| Value | Always positive or zero. | Can be positive, negative, or zero depending on the direction. |
| Path Consideration | Distance considers the actual path traveled by an object. | Displacement considers only the initial and final positions of the object. It ignores the path traveled. |
| Example 1 | If a car travels 10 m east, then 5 m west, the total distance is 15 m. | The displacement is 5 m east (straight-line distance). |
| Example 2 | A runner completes one full lap on a circular track of radius of 10 m. The distance is $2\pi r = 62.8m$. | The displacement is 0 m (same initial and final positions). |
| Path Dependence | Distance is depends on the actual path taken by the object. | Displacement is independent of the path; and depends only on the start and end points. |
| Magnitude | Distance is always greater than or equal to displacement. | Displacement is always less than or equal to distance. |
| Applications | Useful for measuring total travel in real-life activities. | Useful for solving physics problems involving direction (e.g., velocity, motion). |