A car travels half the distance with a constant velocity of `40 m//s` and the remaining half with a constant velocity of `60 m//s`. The average velocity of the car in `m//s` is

Options

A. `42`
B. `50`
C. `48`
D. `45`

Answer

To find the average velocity of the car that travels half the distance at a constant velocity of 40 m/s and the remaining half at 60 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Define the total distance**:
Let's assume the total distance traveled by the car is \(2D\). This means that the car travels a distance \(D\) at 40 m/s and another distance \(D\) at 60 m/s.

2. **Calculate the time taken for each segment**:
- For the first half of the distance \(D\) at 40 m/s, the time taken \(T_1\) can be calculated using the formula:
\[ T_1 = \frac{D}{V_1} = \frac{D}{40} \]
- For the second half of the distance \(D\) at 60 m/s, the time taken \(T_2\) is:
\[ T_2 = \frac{D}{V_2} = \frac{D}{60} \]

3. **Calculate the total time taken**:
The total time \(T\) taken for the entire journey is the sum of \(T_1\) and \(T_2\):
\[ T = T_1 + T_2 = \frac{D}{40} + \frac{D}{60} \]

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

5. **Calculate the average velocity**:
The average velocity \(V_{avg}\) is defined as the total distance divided by the total time:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2D}{T} = \frac{2D}{\frac{D}{24}} = 2D \times \frac{24}{D} = 48 \text{ m/s} \]

### Final Answer:
The average velocity of the car is **48 m/s**.

---