To solve the problem step by step, we will calculate both the average speed and the average velocity of the car during its journey.
### Step 1: Calculate the distance traveled in each direction
The car moves north at a speed of 54 km/h for 1 hour. Therefore, the distance traveled north (D1) is:
\[
D_1 = \text{Speed} \times \text{Time} = 54 \, \text{km/h} \times 1 \, \text{h} = 54 \, \text{km}
\]
Next, the car moves east at the same speed for the same duration. Thus, the distance traveled east (D2) is:
\[
D_2 = 54 \, \text{km/h} \times 1 \, \text{h} = 54 \, \text{km}
\]
### Step 2: Calculate the total distance traveled
The total distance (D_total) is the sum of the distances traveled in both directions:
\[
D_{\text{total}} = D_1 + D_2 = 54 \, \text{km} + 54 \, \text{km} = 108 \, \text{km}
\]
### Step 3: Calculate the total time taken
The total time taken (T_total) for the journey is the sum of the time spent in each direction:
\[
T_{\text{total}} = 1 \, \text{h} + 1 \, \text{h} = 2 \, \text{h}
\]
### Step 4: Calculate the average speed
The average speed (V_avg) is defined as the total distance divided by the total time:
\[
V_{\text{avg}} = \frac{D_{\text{total}}}{T_{\text{total}}} = \frac{108 \, \text{km}}{2 \, \text{h}} = 54 \, \text{km/h}
\]
### Step 5: Calculate the displacement
The displacement is the straight-line distance from the starting point to the final position. The car moves north and then east, forming a right triangle. We can use the Pythagorean theorem to find the magnitude of the displacement (D_displacement):
\[
D_{\text{displacement}} = \sqrt{D_1^2 + D_2^2} = \sqrt{(54 \, \text{km})^2 + (54 \, \text{km})^2}
\]
\[
= \sqrt{2 \times (54 \, \text{km})^2} = 54\sqrt{2} \, \text{km}
\]
### Step 6: Calculate the average velocity
The average velocity (V_avg_velocity) is defined as the total displacement divided by the total time:
\[
V_{\text{avg velocity}} = \frac{D_{\text{displacement}}}{T_{\text{total}}} = \frac{54\sqrt{2} \, \text{km}}{2 \, \text{h}} = 27\sqrt{2} \, \text{km/h}
\]
### Summary of Results
- Average Speed = 54 km/h
- Average Velocity = \( 27\sqrt{2} \, \text{km/h} \) (approximately 38.29 km/h)
