A body goes from A to b with a velocity of 20m/s and comes back from B to A with a velocity of 30m/s. The average velocity of the body during he whole journey is

Options

A. zero
B. 25m/s
C. 24m/s
D. none of these

Explanation

To find the average velocity of the body during the whole journey, we can follow these steps:

### Step 1: Understand the Journey
The body travels from point A to point B and then returns from point B to point A.

### Step 2: Calculate Total Displacement
Displacement is defined as the shortest distance from the initial position to the final position. Since the body starts at point A and returns to point A, the total displacement is:
- **Displacement = Final Position - Initial Position = A - A = 0 m**

### Step 3: Calculate Total Time Taken
To find the total time taken for the journey, we need to calculate the time for each leg of the trip.

1. **From A to B:**
- Velocity = 20 m/s
- Let the distance from A to B be \( d \).
- Time taken from A to B = \( \frac{d}{20} \) seconds.

2. **From B to A:**
- Velocity = 30 m/s
- Time taken from B to A = \( \frac{d}{30} \) seconds.

Now, we can find the total time taken for the whole journey:
- **Total Time = Time from A to B + Time from B to A**
- **Total Time = \( \frac{d}{20} + \frac{d}{30} \)**

To add these fractions, we need a common denominator:
- The least common multiple of 20 and 30 is 60.
- Convert the fractions:
- \( \frac{d}{20} = \frac{3d}{60} \)
- \( \frac{d}{30} = \frac{2d}{60} \)

Now, add them:
- **Total Time = \( \frac{3d}{60} + \frac{2d}{60} = \frac{5d}{60} = \frac{d}{12} \) seconds.**

### Step 4: Calculate Average Velocity
Average velocity is defined as total displacement divided by total time taken:
- **Average Velocity = \( \frac{\text{Total Displacement}}{\text{Total Time}} \)**
- **Average Velocity = \( \frac{0}{\frac{d}{12}} = 0 \) m/s.**

### Final Answer
The average velocity of the body during the whole journey is **0 m/s**.

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