An athlete completes one round of a circular track of radius R in 20 second. What will be his displacement at the end of 2 minute 20 second?

Options

A. Zero
B. 2R
C. 2nR
D. 7nR

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Problem
An athlete completes one round of a circular track of radius \( R \) in 20 seconds. We need to find the displacement after 2 minutes and 20 seconds.

### Step 2: Convert Time to Seconds
First, we convert 2 minutes and 20 seconds into seconds:
\[ 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} \]
Adding the additional 20 seconds:
\[ 120 \text{ seconds} + 20 \text{ seconds} = 140 \text{ seconds} \]

### Step 3: Determine the Number of Complete Rounds
Next, we need to find out how many complete rounds the athlete has completed in 140 seconds. Since the athlete takes 20 seconds to complete one round:
\[ \text{Number of rounds} = \frac{140 \text{ seconds}}{20 \text{ seconds/round}} = 7 \text{ rounds} \]

### Step 4: Analyze the Displacement
After completing 7 full rounds, the athlete returns to the starting point of the circular track. The displacement is defined as the shortest distance from the initial position to the final position.

Since the athlete starts and ends at the same point after 7 rounds:
\[ \text{Displacement} = 0 \]

### Final Answer
Thus, the displacement of the athlete at the end of 2 minutes and 20 seconds is:
\[ \text{Displacement} = 0 \]

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