An athlete complete one round of a circular track of diameter `200 m` in `40 s`. What will be the distance covered and the displacement at the end of `2` minutes `20 s` ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Circumference of the Circular Track
The circumference \( C \) of a circular track can be calculated using the formula:
\[ C = \pi \times d \]
where \( d \) is the diameter of the circular track.

Given:
- Diameter \( d = 200 \, \text{m} \)

Substituting the value:
\[ C = \pi \times 200 = \frac{22}{7} \times 200 \approx 628.57 \, \text{m} \]

### Step 2: Convert Total Time from Minutes and Seconds to Seconds
The total time given is \( 2 \) minutes \( 20 \) seconds. We need to convert this into seconds.
\[ \text{Total time} = 2 \times 60 + 20 = 120 + 20 = 140 \, \text{s} \]

### Step 3: Calculate the Number of Rounds Completed
To find the number of rounds completed by the athlete, we divide the total time by the time taken to complete one round.
Given:
- Time taken for one round \( t_1 = 40 \, \text{s} \)

Calculating the number of rounds:
\[ \text{Number of rounds} = \frac{\text{Total time}}{t_1} = \frac{140}{40} = 3.5 \]

### Step 4: Calculate the Distance Covered
The distance covered by the athlete can be calculated by multiplying the number of rounds by the circumference of the track.
\[ \text{Distance covered} = \text{Number of rounds} \times C = 3.5 \times 628.57 \approx 2200 \, \text{m} \]

### Step 5: Calculate the Displacement
Displacement is defined as the shortest distance from the initial position to the final position. Since the athlete completes 3.5 rounds, they end up halfway around the track from the starting point. The displacement will be equal to the diameter of the circle.
\[ \text{Displacement} = d = 200 \, \text{m} \]

### Final Results
- Distance Covered: \( 2200 \, \text{m} \)
- Displacement: \( 200 \, \text{m} \)

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