Question

An object has moved through a distance can it have zero displacement if yes support your answer with an example.

Answer 1

Yes, an object can have zero displacement even after moving through a distance. Displacement is a vector quantity that measures the shortest straight-line distance from the initial position to the final position, along with direction. Distance, on the other hand, is a scalar quantity that represents the total path length traveled, regardless of direction. If an object returns to its starting point after moving, its displacement is zero because the initial and final positions are the same, even though it covered a non-zero distance.

Example: Suppose you walk 5 meters north from your house to a park, then turn around and walk 5 meters south back to your house. The total distance traveled is 10 meters (5 meters north + 5 meters south). However, the displacement is zero because you end up at the same position where you started (your house), so the net change in position is zero.

Additional Example for Clarity: Imagine running one complete lap around a 400-meter circular track. You cover a distance of 400 meters, but your displacement is zero because you return to your starting point on the track.

Answer 2

1. Understanding the Concepts:

• Distance: The total path length covered by an object during its motion, irrespective of the direction.
• Displacement: The straight-line distance between the initial and final positions of the object, along with the direction. Displacement is a vector quantity, meaning it has both magnitude and direction.

2. Can an object have zero displacement?

Yes, an object can have zero displacement even if it has covered a certain distance. This happens when the object's final position coincides with its initial position. The displacement is calculated as:

\[ \text{Displacement} = \vec{r}_f - \vec{r}_i \] where \(\vec{r}_f\) is the final position vector, and \(\vec{r}_i\) is the initial position vector.

If the initial and final positions are the same, then:

\[ \text{Displacement} = \vec{r}_f - \vec{r}_i = 0 \]

3. Example:

Consider a person who walks 5 meters north and then returns 5 meters south to their original position. The total distance traveled is:

\[ \text{Total Distance} = 5 \, \text{m} + 5 \, \text{m} = 10 \, \text{m} \]

However, the displacement is:

\[ \text{Displacement} = 0 \, \text{m} \, (\text{since the final position is the same as the initial position}) \]

Conclusion: Even though the object has moved a distance of 10 meters, its displacement is zero because the final position coincides with the initial position.