A vehicle moves for 10 minutes at `20 "ms"^(-1)` due north and stops for five minutes. Then at continues due north at `40ms^(-1)` for 20 minutes. Average velocity in the entire journey.

Options

A. `2.857 "ms"^(-1)`
B. `285.7 "ms"^(-1)`
C. `28.57 "ms"^(-1)`
D. `2857 "ms"^(-1)`

Answer

To find the average velocity of the vehicle during its entire journey, we will follow these steps:

### Step 1: Calculate the distance traveled during the first segment
The vehicle moves at a speed of \(20 \, \text{m/s}\) for \(10\) minutes.

- Convert minutes to seconds:
\[ 10 \, \text{minutes} = 10 \times 60 = 600 \, \text{seconds} \]

- Calculate the distance for the first segment (\(s_1\)):
\[ s_1 = \text{speed} \times \text{time} = 20 \, \text{m/s} \times 600 \, \text{s} = 12000 \, \text{meters} \]

### Step 2: Calculate the distance traveled during the second segment
The vehicle then stops for \(5\) minutes, which does not contribute to distance.

Next, it moves at \(40 \, \text{m/s}\) for \(20\) minutes.

- Convert minutes to seconds:
\[ 20 \, \text{minutes} = 20 \times 60 = 1200 \, \text{seconds} \]

- Calculate the distance for the second segment (\(s_2\)):
\[ s_2 = \text{speed} \times \text{time} = 40 \, \text{m/s} \times 1200 \, \text{s} = 48000 \, \text{meters} \]

### Step 3: Calculate the total distance traveled
Now, we can find the total distance traveled (\(s_{\text{total}}\)):
\[ s_{\text{total}} = s_1 + s_2 = 12000 \, \text{meters} + 48000 \, \text{meters} = 60000 \, \text{meters} \]

### Step 4: Calculate the total time of the journey
Now, we calculate the total time taken for the journey:

- Time for the first segment: \(10\) minutes
- Time stopped: \(5\) minutes
- Time for the second segment: \(20\) minutes

Total time in minutes:
\[ \text{Total time} = 10 + 5 + 20 = 35 \, \text{minutes} \]

Convert total time to seconds:
\[ \text{Total time in seconds} = 35 \times 60 = 2100 \, \text{seconds} \]

### Step 5: Calculate the average velocity
Average velocity (\(v_{\text{avg}}\)) is given by the formula:
\[ v_{\text{avg}} = \frac{\text{Total distance}}{\text{Total time}} = \frac{60000 \, \text{meters}}{2100 \, \text{seconds}} \approx 28.57 \, \text{m/s} \]

### Final Answer
The average velocity of the vehicle during the entire journey is approximately \(28.57 \, \text{m/s}\).

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