Can Displacement Be Zero Even When Distance Is Not Zero?

In physics, displacement and distance are two important concepts that describe the motion of an object. Although they are related, they have distinct definitions and meanings. One common question that arises is whether displacement can be zero even when distance is not zero.

The answer is yes — displacement can be zero even when the distance traveled by an object is not zero. To understand this, let’s explore the definitions and differences between displacement and distance, and then look at examples that illustrate this concept.

1. Understanding Displacement and Distance

1.1 Distance

• Distance refers to the total length of the path traveled by an object, regardless of the direction. It is a scalar quantity, meaning it only has magnitude (how much ground the object has covered) and no direction.
• Distance is always positive and cannot be negative, because it only considers the path length.

1.2 Displacement

• Displacement refers to the shortest straight-line distance between an object’s initial and final position, along with the direction of the straight line. It is a vector quantity, meaning it has both magnitude and direction.
• Displacement takes into account not only the distance traveled but also the direction of movement. If the initial and final positions are the same, the displacement is zero, regardless of the path taken.

2. When Can Displacement Be Zero Even if Distance Is Not Zero?

The key to answering this question lies in understanding the relationship between the initial position, final position, and the path taken.

2.1 Path Reversal

If an object moves in a certain direction and then returns to its starting point, the displacement will be zero, even though the distance traveled will be non-zero. This happens because displacement only depends on the initial and final positions, not the path taken.

Example 1: A Round Trip

• Scenario: Suppose a person walks 10 meters forward, then turns around and walks 10 meters back to the starting point.
• Distance: The total distance covered is 10 meters forward + 10 meters back = 20 meters.
• Displacement: The initial and final positions are the same, so the displacement is zero.

In this example, the distance is non-zero (20 meters), but the displacement is zero because the person ended up at the same position where they started.

2.2 Circular Path

If an object moves in a circular path and returns to the starting point, the displacement will be zero, even though the distance traveled will be the length of the entire circle.

Example 2: Circular Motion

• Scenario: Suppose a car drives around a circular track and returns to its starting point.
• Distance: The total distance covered by the car will be the circumference of the circle, which is non-zero.
• Displacement: Since the car returns to its starting point, the displacement is zero because there is no change in the car’s position.

2.3 Back-and-Forth Motion

If an object moves back and forth along the same path, returning to the starting point multiple times, the displacement will still be zero, while the distance traveled will accumulate each time the object moves.

Example 3: Oscillating Motion

• Scenario: A pendulum swings back and forth, starting from one extreme to the other and then returning to the starting point.
• Distance: The total distance traveled by the pendulum is the total length of the path traveled during each swing.
• Displacement: At any point when the pendulum returns to its initial position, the displacement will be zero because there is no net change in its position.

2.4 Straight-Line Motion with No Change in Position

If an object moves along a straight path but ends up back at the same point, the displacement will be zero, even if it has traveled a non-zero distance.

Example 4: Moving in a Straight Line

• Scenario: A person walks 10 meters to the east and then walks 10 meters to the west.
• Distance: The total distance traveled is 10 meters east + 10 meters west = 20 meters.
• Displacement: Since the person ends up back at the starting point, the displacement is zero.

3. Key Differences Between Displacement and Distance

• Distance is a scalar quantity and only measures the total length of the path covered by the object. It is always non-negative and depends solely on the length of the path, not the direction.
• Displacement is a vector quantity and represents the shortest straight-line distance from the initial position to the final position, along with the direction. It can be zero if the initial and final positions are the same, even if the object travels a long distance.

4. Conclusion

In conclusion, displacement can be zero even when the distance traveled is not zero. This happens when the object returns to its starting point after moving along a path, such as in cases of back-and-forth motion, circular motion, or round trips. While distance always measures the total path length, displacement only considers the change in position and can be zero if the object ends up at the same position where it started.

Understanding the difference between distance and displacement is crucial for analyzing motion in physics, as these two quantities provide distinct insights into how objects move through space.