can a particle have zero displacement and non-zero velocity? if yes or no...why so?

Yes, a particle can indeed have zero displacement while maintaining a non-zero velocity. This scenario often arises in the context of circular motion or oscillatory motion, where the particle's position may return to its starting point, resulting in zero displacement, yet it can still be moving at a certain speed. Let’s break this down further to clarify how this works.

Understanding Displacement and Velocity

To grasp this concept, it's essential to differentiate between displacement and velocity:

• Displacement is a vector quantity that refers to the change in position of an object. It is defined as the shortest distance from the initial position to the final position, along with the direction.
• Velocity is also a vector quantity, representing the rate of change of displacement with respect to time. It indicates both the speed and direction of an object’s motion.

Zero Displacement Explained

When we say a particle has zero displacement, it means that the particle has returned to its original position. For example, consider a particle moving in a circular path. If it starts at point A, travels around the circle, and returns to point A, the displacement is zero because the initial and final positions are the same.

Non-Zero Velocity in Circular Motion

Even though the displacement is zero in this case, the particle can have a non-zero velocity. This is because velocity depends on how fast the particle is moving and in what direction. As the particle moves along the circular path, it is continuously changing direction, which means it is still in motion. The speed (magnitude of velocity) can be constant, and thus the velocity is non-zero.

Real-World Example

Let’s consider a practical example: a Ferris wheel. When a passenger rides the Ferris wheel, they start at the bottom and move up, then around, and finally back down to the same starting point. Throughout this journey, the displacement is zero when they return to the starting position, but the passenger has been moving at a certain speed, indicating a non-zero velocity.

Oscillatory Motion

Another example can be found in oscillatory motion, such as a pendulum. When the pendulum swings back and forth, it reaches the same height on either side of its resting position. At the extreme points of its swing, the displacement from the center is maximum, but at the center, where it momentarily stops, the displacement is zero. However, as it passes through the center, it has maximum speed, demonstrating non-zero velocity.

Conclusion

In summary, a particle can have zero displacement while exhibiting non-zero velocity, particularly in scenarios involving circular or oscillatory motion. This distinction highlights the importance of understanding the definitions and relationships between displacement and velocity in physics. By recognizing these concepts, we can better analyze and interpret various types of motion in our world.