A person walks on a straight road from his home to a market 3 km away with a speed of 5 km/h. Finding market closed, he instantaneously turns and walks back with a speed of 6 km/h. The magnitude of average velocity is

Options

A. zero
B. 2.73 km/h
C. 5.45 km/h
D. 5.5 km/h

Explanation

To solve the problem, we need to find the average velocity of a person who walks to a market and then returns home. Here are the steps to calculate the average velocity:

### Step 1: Understand the Motion
The person walks from home to the market, which is 3 km away. After reaching the market, he finds it closed and turns back to walk home.

### Step 2: Calculate Total Displacement
Displacement is defined as the change in position from the initial point to the final point. Since the person returns to his starting point (home), the total displacement is:
\[ \text{Total Displacement} = \text{Final Position} - \text{Initial Position} = 0 \text{ km} \]

### Step 3: Calculate Total Time Taken
Next, we need to calculate the total time taken for the entire journey.

1. **Time to walk to the market:**
- Distance = 3 km
- Speed = 5 km/h
- Time = Distance / Speed = \( \frac{3 \text{ km}}{5 \text{ km/h}} = 0.6 \text{ hours} \)

2. **Time to walk back home:**
- Distance = 3 km
- Speed = 6 km/h
- Time = Distance / Speed = \( \frac{3 \text{ km}}{6 \text{ km/h}} = 0.5 \text{ hours} \)

3. **Total time taken:**
\[ \text{Total Time} = \text{Time to market} + \text{Time to return} = 0.6 \text{ hours} + 0.5 \text{ hours} = 1.1 \text{ hours} \]

### Step 4: Calculate Average Velocity
Average velocity is defined as total displacement divided by total time:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 \text{ km}}{1.1 \text{ hours}} = 0 \text{ km/h} \]

### Conclusion
The magnitude of the average velocity of the person is **0 km/h**.

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