A body covers half the distance with a speed of 20m/s the other half with a speed of 30m/s. The average velocity ogf the body during the whole journey is

Options

A. zero
B. 24m/s
C. ( 25 m/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: Define the total distance
Let the total distance covered by the body be \( S \). Since the body covers half the distance at one speed and the other half at another speed, each half of the distance will be \( \frac{S}{2} \).

### Step 2: Calculate the time taken for each half of the journey
1. **Time for the first half** (\( T_1 \)):
- Distance = \( \frac{S}{2} \)
- Speed = 20 m/s
- Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \):
\[ T_1 = \frac{\frac{S}{2}}{20} = \frac{S}{40} \text{ seconds} \]

2. **Time for the second half** (\( T_2 \)):
- Distance = \( \frac{S}{2} \)
- Speed = 30 m/s
- Using the same formula:
\[ T_2 = \frac{\frac{S}{2}}{30} = \frac{S}{60} \text{ seconds} \]

### Step 3: Calculate the total time for the journey
The total time \( T \) taken for the journey is the sum of the times for both halves:
\[ T = T_1 + T_2 = \frac{S}{40} + \frac{S}{60} \]

### Step 4: Find a common denominator to add the times
The least common multiple of 40 and 60 is 120. Therefore, we can rewrite the times:
\[ T = \frac{3S}{120} + \frac{2S}{120} = \frac{5S}{120} = \frac{S}{24} \text{ seconds} \]

### Step 5: Calculate the average velocity
The average velocity \( V_{avg} \) is defined as the total displacement divided by the total time. Since the total displacement is equal to the total distance \( S \):
\[ V_{avg} = \frac{S}{T} = \frac{S}{\frac{S}{24}} = 24 \text{ m/s} \]

### Final Answer:
The average velocity of the body during the whole journey is **24 m/s**.

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