Average Velocity:
To find the magnitude of average velocity, we need to calculate the displacement of the particle over a given time interval.

Given:
Radius of the circle, R = 21/22 m
Constant speed, v = 1 m/s
Time interval, t = 2 s

The particle is moving in a circle, so its displacement is equal to the length of the arc it travels. The length of an arc on a circle is given by the formula:

Arc Length = θ * R

Where θ is the angle subtended by the arc at the center of the circle.

In this case, the particle travels a full circle, which corresponds to an angle of 2π radians. So, the displacement of the particle is:

Displacement = 2π * R

Now, we can calculate the magnitude of average velocity by dividing the displacement by the time interval:

Average Velocity = Displacement / Time Interval

Average Velocity = (2π * R) / t

Substituting the given values:

Average Velocity = (2π * (21/22)) / 2

Simplifying:

Average Velocity = (21/11)π m/s

Therefore, the magnitude of average velocity is (21/11)π m/s.

Average Acceleration:
To find the magnitude of average acceleration, we need to calculate the change in velocity of the particle over the given time interval.

Since the particle is moving in a circle with constant speed, its velocity is always tangential to the circle at any point. Therefore, the change in velocity is equal to the change in direction.

The change in direction can be calculated using the formula:

Change in Direction = θ

Where θ is the angle subtended by the arc at the center of the circle.

In this case, the particle travels a full circle, which corresponds to an angle of 2π radians. So, the change in direction is:

Change in Direction = 2π

Now, we can calculate the magnitude of average acceleration by dividing the change in velocity by the time interval:

Average Acceleration = Change in Direction / Time Interval

Average Acceleration = (2π) / t

Substituting the given value:

Average Acceleration = (2π) / 2

Simplifying:

Average Acceleration = π rad/s^2

Therefore, the magnitude of average acceleration is π rad/s^2.