Displacement

Understand displacement as the shortest straight-line change in position, with simple examples.

1. What Is Displacement?

Displacement is the shortest straight-line distance between the initial position and the final position of an object. It tells us how far the object has moved and in which direction.

It does not depend on the path taken, only on the starting point and ending point.

1.1. Straight-Line Change in Position

Even if an object moves in a zig-zag or curved path, the displacement is still the straight-line distance connecting the start and end points.

1.2. Direction Is Important

Displacement is a vector quantity. That means it has both magnitude and direction. For example, saying “5 meters east” is a displacement.

2. Displacement Can Be Positive, Negative, or Zero

Because displacement considers direction, its value may sometimes be positive, sometimes negative, and sometimes zero.

2.1. Positive Displacement

If you choose the forward direction as positive, then moving forward gives a positive displacement.

2.2. Negative Displacement

If you move in the opposite direction of your chosen positive direction, the displacement becomes negative.

2.3. Zero Displacement

If the starting and ending positions are the same, displacement becomes zero even if the object has moved.

3. Simple Examples of Displacement

Understanding displacement becomes easy when you compare the start and end points.

3.1. Forward and Backward Walking

If you walk 8 meters forward and 8 meters back to your starting point, the displacement is:

\( 0 \text{ meters} \)

Your final position is the same as the start.

3.2. Walking Along a Curved Path

Even if you take a curved road from point A to point B, the displacement is just the straight-line distance from A to B.

3.3. Around a Circular Track

If you complete one full circle and return to your starting point, the displacement is again:

\( 0 \text{ meters} \)

4. Formula for Displacement in Straight-Line Motion

When an object moves in a straight line, and directions are marked as positive and negative, displacement can be written simply as:

\( \text{Displacement} = x_{\text{final}} - x_{\text{initial}} \)

4.1. Example

If a car moves from 2 m to 12 m on a straight road, the displacement is:

\( 12 - 2 = 10 \text{ meters} \)

5. Displacement Does Not Depend on Path

This is the biggest difference between distance and displacement:

Distance → depends on path.
Displacement → depends only on start and end positions.

5.1. Example Showing Path vs Straight Line

If you take a long curved path to reach a shop 200 meters away, your distance may be 250 meters or more. But the displacement is still:

\( 200 \text{ meters (straight-line)} \)