No, distance is not always equal to displacement.
Understanding the difference between distance and displacement is fundamental in physics. Displacement is the shortest path travelled. This means that it can be the same as the distance only if the distance itself is the shortest path, else the distance will be greater than displacement.
Understanding Distance
Distance refers to the total length of the path covered by an object during its motion, regardless of the direction. It is a scalar quantity, meaning it only has magnitude. Think of it as the odometer reading in a car – it just adds up the total mileage.
Understanding Displacement
Displacement, on the other hand, is the change in an object's position from its starting point to its ending point. It is the straight-line distance between the initial and final positions, along with the direction. Displacement is a vector quantity, possessing both magnitude and direction.
When Distance Equals Displacement
As stated in the definition, displacement is equal to distance only when the path taken is the shortest path between the two points. This typically occurs when an object moves in a straight line without changing direction.
- Example: If you walk 10 meters directly north from point A to point B, your distance covered is 10 meters, and your displacement is also 10 meters north.
When Distance is Greater Than Displacement
In most other scenarios, the distance covered will be greater than the magnitude of the displacement. This happens whenever the path taken is not a straight line or when the object changes direction during its movement.
- Example 1: Winding Path: If you travel from point A to point B along a winding road, the distance you cover (the length of the road) will be much longer than the displacement (the straight-line distance from A to B).
- Example 2: Round Trip: If you walk from your house to the park and then back to your house, your total distance covered is the length of the trip to the park plus the length of the trip back. However, since you ended up at your starting point, your displacement is zero.
- Example 3: Changing Direction: If you walk 5 meters north and then 5 meters east, your total distance is 10 meters. Your displacement, however, would be the straight-line distance from your start to end point (which would be the hypotenuse of a right triangle, approximately 7.07 meters, in a north-east direction).
Key Differences: Distance vs. Displacement
Here's a simple comparison:
| Feature | Distance | Displacement |
|---|---|---|
| Type | Scalar (Magnitude only) | Vector (Magnitude and Direction) |
| What it Measures | Total path length traveled | Change in position (shortest path between start/end) |
| Value | Always positive or zero | Can be positive, negative, or zero |
| Comparison | Always greater than or equal to displacement | Always less than or equal to distance |
In summary, distance tracks the entire journey's length, while displacement only cares about the net change in location. They are the same only in the special case of straight-line motion without a change in direction.
