Angular acceleration is the rate at which the angular velocity of an object changes with time. It is denoted by the symbol α. In order to determine the value of angular acceleration, we need to consider the linear acceleration and the radius of the circular path.

Linear Acceleration:
The linear acceleration is given as 5 m/s². This means that the speed of the particle is increasing by 5 m/s every second in the direction of motion.

Radius of the Circular Path:
The radius of the circular path is given as 2 m. This represents the distance between the center of the circle and the particle.

Relation between Linear and Angular Acceleration:
The linear acceleration and angular acceleration are related by the equation:

a = rα

where a is the linear acceleration, r is the radius of the circular path, and α is the angular acceleration.

Calculating Angular Acceleration:
Substituting the given values, we have:

5 m/s² = 2 m * α

Simplifying the equation, we find:

α = 5 m/s² / 2 m

α = 2.5 rad/s²

Therefore, the value of angular acceleration is 2.5 rad/s².

Explanation:
When a particle moves in a circular path, it experiences a centripetal acceleration towards the center of the circle. This centripetal acceleration is related to the linear acceleration through the equation a = rα. In this case, the linear acceleration is given as 5 m/s² and the radius of the circular path is 2 m. By substituting these values into the equation, we can solve for the angular acceleration. The resulting value of 2.5 rad/s² indicates that the particle's angular velocity is increasing at a rate of 2.5 radians per second squared.