A man leaves his house for a cycle ride. He comes back to his house after half-an-hour after covering a distance of one km. What is his average velocity for the ride?

Options

A. zero
B. `2 km h^(-1)`
C. `10 km s^(-1)`
D. `(1)/(2) km h^(-1)`

Explanation

To solve the problem, we need to determine the average velocity of the man during his cycle ride. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Definitions
- **Displacement** is the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction.
- **Average Velocity** is defined as the total displacement divided by the total time taken.

### Step 2: Analyze the Given Information
- The man leaves his house and returns after half an hour (30 minutes).
- The total distance covered during the ride is 1 km.

### Step 3: Calculate the Displacement
- Since the man returns to his starting point (his house), the net displacement is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 \text{ km} \]

### Step 4: Calculate the Total Time Taken
- The total time taken for the ride is given as 30 minutes, which can be converted to hours for convenience:
\[ \text{Total Time} = 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]

### Step 5: Calculate the Average Velocity
- Using the formula for average velocity:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 \text{ km}}{0.5 \text{ hours}} = 0 \text{ km/h} \]

### Conclusion
The average velocity of the man during his cycle ride is:
\[ \text{Average Velocity} = 0 \text{ km/h} \]