Usha swims in a `90 m` long pool. She covers `180 m` in one minute by swimming from one end to the other and back along the same length path. Find the average speed and average speed and average velocity of Usha.

Explanation

To solve the problem, we need to calculate Usha's average speed and average velocity based on the information provided.

### Step-by-Step Solution:

1. **Identify the Total Distance Covered**:
- Usha swims from one end of the pool to the other and back.
- The length of the pool is `90 m`.
- Therefore, the total distance covered when she swims to one end and back is:
\[ \text{Total Distance} = 90 \, \text{m} + 90 \, \text{m} = 180 \, \text{m} \]

2. **Determine the Total Time Taken**:
- It is given that Usha takes `1 minute` to cover this distance.
- We need to convert this time into seconds for our calculations:
\[ \text{Total Time} = 1 \, \text{minute} = 60 \, \text{seconds} \]

3. **Calculate Average Speed**:
- Average speed is defined as the total distance covered divided by the total time taken.
- Using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{180 \, \text{m}}{60 \, \text{s}} = 3 \, \text{m/s} \]

4. **Calculate Average Velocity**:
- Average velocity is defined as the net displacement divided by the total time taken.
- The net displacement is the difference between the final position and the initial position. Since Usha returns to her starting point:
\[ \text{Net Displacement} = 0 \, \text{m} \]
- Therefore, using the formula:
\[ \text{Average Velocity} = \frac{\text{Net Displacement}}{\text{Total Time}} = \frac{0 \, \text{m}}{60 \, \text{s}} = 0 \, \text{m/s} \]

### Final Answers:
- **Average Speed**: \(3 \, \text{m/s}\)
- **Average Velocity**: \(0 \, \text{m/s}\)