1. What Makes Distance and Displacement Different?
Distance and displacement both describe how far an object has moved, but they are not the same. Distance tells us the total path covered. Displacement tells us the shortest straight-line change in position.
1.1. Path-Based vs Straight-Line
Distance depends on the path taken. If you walk in a zig-zag way, distance increases. Displacement only looks at where you started and where you ended.
1.2. Scalar vs Vector
Distance is a scalar quantity (only magnitude). Displacement is a vector quantity (magnitude + direction).
2. Comparison Table
| Distance | Displacement |
|---|---|
| Total path length covered by an object. | Shortest straight-line distance between start and end points. |
| Depends on path taken. | Does not depend on path taken. |
| Always positive or zero. | Can be positive, negative, or zero. |
| Scalar quantity (only magnitude). | Vector quantity (magnitude + direction). |
| Never decreases as an object moves. | Can increase, decrease, or become zero. |
3. Understanding with Simple Cases
These examples help you clearly see why distance and displacement are often different.
3.1. Case 1: Walking in a Straight Line
If you walk 50 meters from point A to point B:
- Distance = 50 m
- Displacement = 50 m (straight line)
3.2. Case 2: Going Forward and Returning Back
If you walk 30 meters forward and then come back 30 meters to your starting point:
- Distance = 30 + 30 = 60 m
- Displacement = 0 m (final position = initial position)
3.3. Case 3: Moving Along a Curved Path
You move along a curved road for 120 meters to reach a point that is only 80 meters away in a straight line:
- Distance = 120 m
- Displacement = 80 m
3.4. Case 4: Completing a Circular Lap
If you run one complete round on a circular track and return to the same point:
- Distance = Circumference of the track
- Displacement = 0 m
4. When Distance and Displacement Become Equal
Distance and displacement become equal only in one situation: when the object moves in a perfectly straight line without changing direction.
4.1. Example
A train moving straight from Station A to Station B covers 10 km:
- Distance = 10 km
- Displacement = 10 km
5. When Distance Is Greater Than Displacement
This is the most common situation. Whenever the path is not straight or the object returns toward the starting point, distance becomes greater.
5.1. Example
If you walk to the market taking a roundabout way, the distance may be 2 km. But the shortest straight-line distance (displacement) may be only 1.2 km.