**Displacement of a particle moving in a circle**

When a particle moves in a circle, its displacement is the straight line distance from the initial position to the final position. In this case, the particle is moving in a circle of diameter 5m. To determine the displacement when it covers one and a half revolutions, we need to consider a few key points.

**Understanding the problem**

- The diameter of the circle is given as 5m, which means the radius of the circle is half of the diameter, i.e., 2.5m.
- One revolution refers to the particle completing a full circle around the circumference.
- One and a half revolutions means the particle completes one full circle and then covers half of another revolution.

**Calculating the displacement**

To find the displacement, we need to determine the initial and final positions of the particle.

**Initial Position:**
- The initial position of the particle is the starting point of its motion.
- Since the particle completes one full revolution, its initial position can be any point on the circumference of the circle.

**Final Position:**
- The final position of the particle is the point where it ends its motion.
- Since the particle covers one and a half revolutions, its final position will be half the circumference of the circle plus half of the remaining distance.
- The circumference of a circle is given by the formula C = 2πr, where r is the radius.
- In this case, the circumference is C = 2π(2.5m) = 15.7m.
- Half the circumference is 15.7m/2 = 7.85m.
- The remaining distance to be covered is half of the circumference of the circle, i.e., half of 15.7m = 7.85m.
- Therefore, the final position of the particle is 7.85m + 7.85m = 15.7m.

**Displacement:**
- Displacement is the straight line distance between the initial and final positions of the particle.
- In this case, the displacement is the straight line distance between any point on the circumference of the circle (initial position) and the final position.
- Since the particle completes one and a half revolutions, it ends up at the point diametrically opposite to the initial position.
- This means the displacement is equal to the diameter of the circle, which is 5m.

Therefore, the displacement of the particle when it covers one and a half revolutions is 5m.

**Summary**
- The particle moves in a circle of diameter 5m.
- One and a half revolutions mean the particle completes one full circle and then covers half of another revolution.
- The initial position can be any point on the circumference of the circle.
- The final position is found by adding half the circumference of the circle and half of the remaining distance to be covered.
- The displacement is the straight line distance between the initial and final positions.
- In this case, the displacement is equal to the diameter of the circle, which is 5m.

5 meter. Because the particle will be exactly opposite to the initial position. and the direct line that joins the both points is the length of the diameter.

Hence the Displacement is 5 Meter