Given:
- Radius of the circular path = 14 m
- Angular displacement of the particle = 135 degrees

To find:
- Distance covered by the particle on the circular path

Solution:

1. Understanding the problem:
In this problem, we are given that a particle is moving on a circular path with a radius of 14 m. The angular displacement of the particle is given as 135 degrees. We need to calculate the distance covered by the particle on the circular path.

2. Understanding the terms:
Before we proceed with the solution, let's understand a few important terms related to circular motion:

- Angular displacement: It is the angle through which an object moves in a circular path. It is measured in radians or degrees.
- Radius: It is the distance from the center of the circle to any point on its circumference.
- Circumference: It is the distance around the boundary of a circle.
- Distance: It is the total length traveled by an object.

3. Calculating the circumference:
The circumference of a circle can be calculated using the formula:

Circumference = 2 * π * radius

Given that the radius of the circular path is 14 m, we can calculate the circumference as:

Circumference = 2 * π * 14

4. Calculating the distance covered:
The distance covered by the particle on the circular path can be calculated using the formula:

Distance = (angular displacement / 360 degrees) * Circumference

Given that the angular displacement is 135 degrees and the circumference is calculated as 2 * π * 14, we can substitute these values in the formula to calculate the distance covered.

Distance = (135 / 360) * (2 * π * 14)

5. Calculating the final result:
Now, let's calculate the distance covered by the particle using the above formula:

Distance = (135 / 360) * (2 * π * 14)
Distance = (3/8) * (2 * 3.14 * 14)
Distance = (3/8) * (6.28 * 14)
Distance = (3/8) * (87.92)
Distance = 32.91 m

Therefore, the distance covered by the particle on the circular path is 32.91 meters.

Summary:
A particle moving on a circular path with a radius of 14 m and an angular displacement of 135 degrees covers a distance of 32.91 meters on the circular path.