A boy completes one round of a circular track of radius r in 40 s. His displacement at the end of 2min 20s will be

Options

A. zero
B. 2r
C. `2pir`
D. `7pir`

Answer

To solve the problem, we need to determine the boy's displacement after he runs for 2 minutes and 20 seconds on a circular track with a radius \( r \).

### Step-by-Step Solution:

1. **Convert Time to Seconds**:
- The total time given is 2 minutes and 20 seconds.
- Convert this to seconds:
\[ 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} \]
\[ 120 \text{ seconds} + 20 \text{ seconds} = 140 \text{ seconds} \]

2. **Determine the Number of Rounds Completed**:
- The boy completes one round of the circular track in 40 seconds.
- To find out how many rounds he completes in 140 seconds, we can calculate:
\[ \text{Number of rounds} = \frac{140 \text{ seconds}}{40 \text{ seconds/round}} = 3.5 \text{ rounds} \]

3. **Identify the Final Position**:
- After completing 3 full rounds, he returns to the starting point (let's call it point A).
- Since he completes 3 rounds in 120 seconds, he has 20 seconds left to run.
- In 20 seconds, he will cover half of the track (since 40 seconds is needed for a full round).
- Therefore, after 3.5 rounds, he ends up at the point directly opposite to point A on the circular track.

4. **Calculate the Displacement**:
- Displacement is defined as the shortest distance between the initial and final positions.
- Since the boy starts at point A and ends up at the point directly opposite A after 3.5 rounds, the displacement is equal to the diameter of the circular track.
- The diameter \( D \) of the circular track is given by:
\[ D = 2r \]
- Thus, the displacement of the boy at the end of 2 minutes and 20 seconds is:
\[ \text{Displacement} = 2r \]

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

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