To determine both the distance covered and the displacement of the athlete after 2 minutes and 20 seconds, we must first understand the physical properties involved in circular motion.
1. **Calculate the Circumference of the Track:**
The circumference (C) of a circle is calculated using the formula:
C = π × d
Where d is the diameter of the circle. In this case, the diameter of the track is 200m, so:
C = π × 200m ≈ 628.32m
2. **Distance Covered in One Round:**
As established, the athlete completes one full round of the track, which means they cover the entire circumference of approximately 628.32 meters in 40 seconds.
3. **Time Duration in Seconds:**
The total time of interest is 2 minutes and 20 seconds. First, convert this to seconds:
2 minutes = 120 seconds20 seconds = 20 seconds
So, total time = 120s + 20s = 140s
4. **Number of Rounds Completed in 140 seconds:**
Next, calculate how many rounds the athlete completes in this total time:
Time per round = 40 seconds
Number of rounds = 140s / 40s = 3.5 rounds
5. **Total Distance Covered:**
To find the total distance covered by the athlete, multiply the number of rounds completed by the circumference of the track:
Total Distance = Number of Rounds × Circumference
Total Distance = 3.5 × 628.32m ≈ 2199.12m
6. **Displacement Calculation:**
Displacement is the shortest distance between the initial and final position of the athlete. Since the athlete completes 3.5 rounds, they end up halfway around the circular track from their starting point.
To determine the displacement, we consider the geometry of the circle. When the athlete is at the halfway point, they are on the direct opposite side of the starting point, which means:
**Displacement = Diameter of the track = 200m**
### Summary
- Total Distance Covered: Approximately 2199.12 meters
- Displacement: 200 meters
Thus, after 2 minutes and 20 seconds, the athlete covers a distance of about 2199.12 meters and has a displacement of 200 meters.