A car moves towards north at a speed of 54 km/h for 1 h. Then jt moves eastward with same speed for same duration . The average speed and velocity of car for complete journey is

Options

A. 54 km/m 0
B. 15 m/s , `(15)/(sqrt(2))` m/s
C. 0,0
D. `0, (54)/(sqrt(2))` km/h

Answer

To solve the problem, we need to calculate the average speed and average velocity of the car over its entire journey. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the distance traveled in each direction.
1. The car moves north at a speed of 54 km/h for 1 hour.
- Distance traveled north = Speed × Time = 54 km/h × 1 h = 54 km.

2. The car then moves east at the same speed for the same duration.
- Distance traveled east = Speed × Time = 54 km/h × 1 h = 54 km.

### Step 2: Calculate the total distance traveled.
- Total distance = Distance north + Distance east = 54 km + 54 km = 108 km.

### Step 3: Calculate the total time taken.
- Total time = Time north + Time east = 1 h + 1 h = 2 h.

### Step 4: Calculate the average speed.
- Average speed = Total distance / Total time = 108 km / 2 h = 54 km/h.

### Step 5: Calculate the average velocity.
1. The average velocity is defined as the total displacement divided by the total time.
2. The displacement can be calculated using the Pythagorean theorem since the car moves north and then east, forming a right triangle.
- Displacement = √(Distance north² + Distance east²) = √(54² + 54²) = √(2916 + 2916) = √(5832) = 54√2 km.

3. Now, calculate the average velocity.
- Average velocity = Total displacement / Total time = (54√2 km) / 2 h = 27√2 km/h.

### Final Answers:
- Average Speed = 54 km/h
- Average Velocity = 27√2 km/h (approximately 38.29 km/h)