An athelete completes one round of a circular track of radius `R` in 40 seconds. What will be the displacement at the end of ` 2 min. 20 second ?

Options

A. zero
B. 2R
C. `2piR`
D. `7pR`

Answer

To solve the problem, we need to determine the displacement of the athlete after completing a certain amount of time on a circular track.

### Step-by-Step Solution:

1. **Convert the total time into seconds:**
- The total time given is 2 minutes and 20 seconds.
- Convert 2 minutes into seconds:
\[ 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} \]
- Add the remaining 20 seconds:
\[ \text{Total time} = 120 \text{ seconds} + 20 \text{ seconds} = 140 \text{ seconds} \]

2. **Determine the number of complete rounds:**
- The athlete completes one round of the circular track in 40 seconds.
- To find the number of complete rounds in 140 seconds, divide the total time by the time per round:
\[ \text{Number of rounds} = \frac{140 \text{ seconds}}{40 \text{ seconds/round}} = 3.5 \text{ rounds} \]

3. **Identify the position after 3 complete rounds:**
- After completing 3 rounds, the athlete will be back at the starting point on the circular track.

4. **Calculate the position after the additional 0.5 round:**
- After completing 3 rounds (which takes 120 seconds), the athlete has 20 seconds left.
- In 20 seconds, the athlete covers half a round (since 20 seconds is half of 40 seconds).
- Starting from the initial position (let's say point A), after 3 rounds, the athlete is back at point A.
- After covering half a round, the athlete will be at the point directly opposite to point A (let's call this point B).

5. **Determine the displacement:**
- The displacement is defined as the shortest distance from the initial position to the final position.
- Since the athlete is now at point B, which is diametrically opposite to point A, the displacement is equal to the diameter of the circular track.
- The diameter \(D\) of the circular track is given by:
\[ D = 2R \]
- Therefore, the displacement after 2 minutes and 20 seconds is \(2R\).

### Final Answer:
The displacement at the end of 2 minutes and 20 seconds is \(2R\).