**Problem Analysis:**

To find the average velocity of a bicycle, we need to determine the total distance traveled and the total time taken. In this problem, the bicycle completes two complete rounds of a circular track with a radius of 140 m. We are given that the time taken to complete this distance is 5 minutes and 52 seconds.

**Solution:**

To find the average velocity, we will follow these steps:

1. Find the total distance traveled by the bicycle.
2. Convert the given time into seconds.
3. Calculate the average velocity using the formula: Average velocity = total distance / total time.

**Step 1: Find the total distance traveled by the bicycle**

The total distance traveled by the bicycle can be calculated by finding the circumference of the circular track and multiplying it by the number of rounds completed.

Circumference of the circular track = 2πr, where r is the radius of the track.

Given radius of the circular track = 140 m

Hence, the circumference of the circular track = 2 * 3.14 * 140 = 879.2 m

Since the bicycle completes two complete rounds, the total distance traveled = 2 * 879.2 = 1758.4 m

**Step 2: Convert the given time into seconds**

Given time = 5 minutes and 52 seconds

To convert minutes into seconds, we multiply it by 60.

Total time in seconds = (5 * 60) + 52 = 352 seconds

**Step 3: Calculate the average velocity**

Average velocity = total distance / total time

Substituting the values, we get:

Average velocity = 1758.4 m / 352 s

= 4.99 m/s (rounded to two decimal places)

**Answer:**

The average velocity of the bicycle is approximately 4.99 m/s.

Average speed of the bicycle = 4.995 that is approximately 5 m/s.