A person takes time t to go once around a circular path of diameter 2 R . The speed (v) of this person would be

Options

A. ` (t)/(2 pi R)`
B. ` (2 pi R)/( t)`
C. `(pi R ^(2))/( t)`
D. `2 pi R t`

Explanation

To find the speed \( v \) of a person who takes time \( t \) to go once around a circular path of diameter \( 2R \), we can follow these steps:

### Step 1: Identify the radius of the circular path
The diameter of the circular path is given as \( 2R \). Therefore, the radius \( r \) can be calculated as:
\[ r = \frac{2R}{2} = R \]

### Step 2: Calculate the circumference of the circular path
The distance traveled by the person in one complete revolution around the circular path is equal to the circumference of the circle. The formula for the circumference \( C \) of a circle is:
\[ C = 2\pi r \]
Substituting the value of \( r \):
\[ C = 2\pi R \]

### Step 3: Use the formula for average speed
The average speed \( v \) is defined as the total distance traveled divided by the total time taken. Thus, we can express the average speed as:
\[ v = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{C}{t} \]
Substituting the value of \( C \):
\[ v = \frac{2\pi R}{t} \]

### Final Answer
The speed \( v \) of the person is:
\[ v = \frac{2\pi R}{t} \]