To determine the distance covered and the displacement of the athlete, we need to analyze the situation step by step.
The diameter of the circular track is given as 200 meters. First, we can find the circumference (which is the distance for one complete round) using the formula:
Circumference = π × Diameter
Substituting the given diameter:
Circumference = π × 200m ≈ 628.32m
The athlete completes one round in 40 seconds, which means that in this time, he has covered the entire circumference of the track, which is approximately 628.32 meters.
Next, let’s find out how many rounds the athlete can complete in 2 minutes and 20 seconds. We first convert 2 minutes and 20 seconds into seconds:
2 minutes = 120 seconds
20 seconds = 20 seconds
Total time = 120s + 20s = 140s
Now, we calculate how many rounds the athlete can complete in 140 seconds:
Rounds completed = Total time / Time per round
Rounds completed = 140s / 40s = 3.5 rounds
Now, to find the distance covered, we multiply the number of rounds completed by the circumference:
Distance covered = Rounds completed × Circumference
Distance covered = 3.5 × 628.32m ≈ 2199.12m
Now, for displacement, we need to note that displacement is the shortest distance from the starting point to the final point. Since the athlete completes 3 full rounds and ends halfway around the track, the final position is directly opposite the start point.
The distance of displacement from the starting point to the opposite point on the circular track is equal to the diameter of the circle:
Displacement = Diameter = 200m
In conclusion, at the end of 2 minutes and 20 seconds, the distance covered by the athlete is approximately 2199.12 meters, while the displacement is 200 meters.