A cyclist moving on a circular track of radius 20m completes half a revolution in 20 seconds.
What is its average velocity?

Options

A. zero
B. `2pims^(-1)`
C. `2ms^(-1)`
D. `4pims^(-1)`

Answer

To find the average velocity of the cyclist moving on a circular track, we can follow these steps:

### Step 1: Understand the Problem
The cyclist completes half a revolution on a circular track with a radius of 20 meters in 20 seconds. We need to calculate the average velocity.

### Step 2: Calculate the Displacement
Displacement is defined as the shortest distance between the initial and final positions. Since the cyclist completes half a revolution, the initial position and final position are at opposite ends of the diameter of the circle.

- The diameter \( D \) of the circular track can be calculated as:
\[ D = 2 \times \text{radius} = 2 \times 20 \, \text{m} = 40 \, \text{m} \]
Thus, the displacement of the cyclist is 40 meters.

### Step 3: Calculate the Time Taken
The time taken to complete half a revolution is given as 20 seconds.

### Step 4: Calculate the Average Velocity
Average velocity is defined as the total displacement divided by the total time taken. We can use the formula:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
Substituting the values we have:
\[ \text{Average Velocity} = \frac{40 \, \text{m}}{20 \, \text{s}} = 2 \, \text{m/s} \]

### Final Answer
The average velocity of the cyclist is \( 2 \, \text{m/s} \).

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