A bird files due north at velocity 20 `ms^(-1)` for 15s it rests for 5s and then files due south at velocity `24 ms^(-1)` for 10s. For the whole trip find the average speed and magnitude of average velocity

Answer

To solve the problem step by step, let's break down the movements of the bird and calculate the average speed and average velocity.

### Step 1: Calculate the total time of the trip
The total time is the sum of the time spent flying north, resting, and flying south.

- Time flying north = 15 seconds
- Time resting = 5 seconds
- Time flying south = 10 seconds

**Total time = 15 s + 5 s + 10 s = 30 s**

### Step 2: Calculate the distance traveled
Next, we calculate the distance covered during each segment of the trip.

1. **Distance flying north:**
- Velocity = 20 m/s
- Time = 15 s
- Distance = Velocity × Time = 20 m/s × 15 s = 300 m

2. **Distance resting:**
- Distance = 0 m (since the bird is at rest)

3. **Distance flying south:**
- Velocity = 24 m/s
- Time = 10 s
- Distance = Velocity × Time = 24 m/s × 10 s = 240 m

**Total distance = Distance north + Distance resting + Distance south = 300 m + 0 m + 240 m = 540 m**

### Step 3: Calculate the displacement
Displacement is the difference between the final position and the initial position. We will consider north as positive.

1. **Displacement flying north:**
- Displacement = +300 m (since it is going north)

2. **Displacement flying south:**
- Displacement = -240 m (since it is going south)

**Total displacement = Displacement north + Displacement south = 300 m - 240 m = 60 m**

### Step 4: Calculate the average speed
Average speed is defined as the total distance traveled divided by the total time taken.

**Average speed = Total distance / Total time = 540 m / 30 s = 18 m/s**

### Step 5: Calculate the average velocity
Average velocity is defined as the total displacement divided by the total time taken.

**Average velocity = Total displacement / Total time = 60 m / 30 s = 2 m/s**

### Final Answers
- Average Speed = 18 m/s
- Magnitude of Average Velocity = 2 m/s

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