A car travels 100 km cast an then 100 km south. Finally, it comes back to the starting point by the shortest route. Throughout the journey, the speed is constant at 60 km/h. The average velocity for the whole of the journey is

Options

A. 60 km/h
B. 90 km/h
C. 0 km/h
D. 180 km/h

Answer

To solve the problem, we need to determine the average velocity of the car after completing its journey. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Journey
The car travels:
- 100 km east
- 100 km south
- Then returns to the starting point by the shortest route.

### Step 2: Determine the Total Displacement
Displacement is defined as the shortest distance from the initial position to the final position.

- The car starts at point O.
- After traveling 100 km east, it reaches point A.
- Then it travels 100 km south to point B.
- Finally, it returns to the starting point O.

Since the car ends up back at the starting point O, the total displacement is:
- Displacement = Final Position - Initial Position = O - O = 0 km

### Step 3: Calculate the Total Distance Traveled
The total distance traveled by the car is the sum of all segments of the journey:
- Distance east = 100 km
- Distance south = 100 km
- Distance back to starting point (which is the hypotenuse of a right triangle formed by the east and south distances).

Using the Pythagorean theorem to find the distance back:
\[ \text{Distance back} = \sqrt{(100^2 + 100^2)} = \sqrt{20000} = 100\sqrt{2} \approx 141.42 \text{ km} \]

Total distance traveled = 100 km + 100 km + 141.42 km = 341.42 km.

### Step 4: Calculate the Total Time Taken
The speed of the car is constant at 60 km/h. To find the total time taken, we use the formula:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} \]
\[ \text{Time} = \frac{341.42 \text{ km}}{60 \text{ km/h}} \approx 5.69 \text{ hours} \]

### Step 5: Calculate the Average Velocity
Average velocity is defined as total displacement divided by total time:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
Since the total displacement is 0 km:
\[ \text{Average Velocity} = \frac{0 \text{ km}}{5.69 \text{ hours}} = 0 \text{ km/h} \]

### Conclusion
The average velocity for the whole journey is **0 km/h**.

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