To find the distance covered and the displacement of the athlete after 2 minutes 20 seconds, let's break down the problem step-by-step.

Step 1: Calculate the Circumference of the Track

Since the track is circular with a diameter of 200 m, we can find its circumference using the formula:

$\text{Circumference} = \pi \times \text{Diameter} = \pi \times 200 \, \text{m}$

$\text{Circumference} = 200\pi \, \text{m} \approx 628.32 \, \text{m}$

Step 2: Find the Total Time in Seconds

The given time is 2 minutes 20 seconds. Convert this time into seconds:

$2 \, \text{minutes} = 2 \times 60 = 120 \, \text{seconds}$

$\text{Total time} = 120 + 20 = 140 \, \text{seconds}$

Step 3: Calculate the Number of Rounds Completed

The athlete completes one round in 40 seconds. To find the number of rounds completed in 140 seconds, divide the total time by the time taken for one round:

$\text{Number of rounds} = \frac{140}{40} = 3.5$

Step 4: Calculate the Total Distance Covered

The distance covered in each round is the circumference of the track. Therefore, the total distance covered is:

$\text{Total distance} = 3.5 \times 200\pi \, \text{m} \approx 3.5 \times 628.32 \, \text{m}$

$\text{Total distance} \approx 2199.12 \, \text{m}$

Step 5: Calculate the Displacement

Displacement is the shortest straight-line distance between the starting and ending points. Since the athlete completes 3.5 rounds, they end up exactly opposite the starting point on the circle's circumference. The displacement is the diameter of the circle:

$\text{Displacement} = 200 \, \text{m}$

Conclusion

• Distance covered: $\approx 2199.12 \, \text{m}$
• Displacement: $200 \, \text{m}$

Would you like further details or have any questions?

Related Questions:

1. How would the distance and displacement change if the time were different?
2. What is the relationship between distance and displacement?
3. How can you calculate the average speed of the athlete?
4. How does the shape of the track affect displacement?
5. What are other examples of scenarios with differing distance and displacement?

Tip: In circular motion, the displacement depends on the position relative to the starting point, not the path taken.