Distance and Displacement of a Particle in Circular Motion

Introduction:
When a particle moves in a circular path, it traces out a distance and experiences a displacement. The distance refers to the total length of the path covered by the particle, while displacement refers to the change in position of the particle from its initial point to its final point.

Given:
- Diameter of the circle = 15 units
- The particle completes two rounds

Calculating Distance:
To calculate the distance covered by the particle, we need to consider the circumference of the circle. The formula to calculate the circumference is given by:
Circumference = π × diameter

Substituting the given diameter value into the formula, we can find the circumference:
Circumference = π × 15
Circumference ≈ 3.14 × 15
Circumference ≈ 47.1 units

Since the particle completes two rounds, we need to multiply the circumference by 2 to find the total distance covered:
Total Distance = 2 × Circumference
Total Distance = 2 × 47.1
Total Distance ≈ 94.2 units

Therefore, the particle covers a distance of approximately 94.2 units.

Calculating Displacement:
The displacement of the particle can be found by considering its initial and final positions. In this case, the particle completes two rounds, which means it returns to its initial position.

The displacement of the particle moving in a circular path and returning to its initial position is always zero. This is because displacement is a vector quantity and takes into account the change in position. Since the initial and final positions coincide for a particle completing multiple rounds, the displacement is zero.

Summary:
- The particle traveling in a circle with a diameter of 15 units covers a total distance of approximately 94.2 units.
- However, since the particle completes two rounds and returns to its initial position, the displacement is zero.
- Distance refers to the total length of the path covered, while displacement refers to the change in position between the initial and final points.
- It is important to consider the concept of displacement, as it provides information about the change in position rather than just the total distance covered.