A particle is moving in a circle of diameter `5m`. Calculate the distance covered and the displacement when it completes `3 ` revolutions.

Explanation

### Step-by-Step Solution:

**Step 1: Understand the problem and given data.**

- Diameter of the circle, \( D = 5 \) meters.
- Number of revolutions, \( n = 3 \).

**Step 2: Calculate the distance covered.**

The distance covered by the particle is the total length of the path it travels. Since the particle is moving in a circle, the distance covered in one revolution is the circumference of the circle.

- The formula for the circumference of a circle is:
\[ \text{Circumference} = \pi \times D \]
where \( D \) is the diameter of the circle.

- For one revolution:
\[ \text{Circumference} = \pi \times 5 \text{ meters} \]

- For three revolutions:
\[ \text{Distance covered} = 3 \times \pi \times 5 \text{ meters} \]

- Simplify the expression:
\[ \text{Distance covered} = 15 \pi \text{ meters} \]

- Approximate the value using \( \pi \approx 3.14 \):
\[ \text{Distance covered} = 15 \times 3.14 \text{ meters} \approx 47.1 \text{ meters} \]

**Step 3: Calculate the displacement.**

Displacement is the shortest distance between the initial and final positions of the particle. Since the particle completes 3 revolutions and returns to its starting point, the initial and final positions are the same.

- Therefore, the displacement is:
\[ \text{Displacement} = 0 \text{ meters} \]

### Final Answer:

- **Distance covered**: \( 47.1 \) meters (approximately).
- **Displacement**: \( 0 \) meters.