An object travels 10km at a speed of 100 m/s and another 10km at 50 m/s. The average speed over the whole distance is:-

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Explanation

To find the average speed of the object over the entire distance, we can follow these steps:

### Step 1: Convert Distance to Meters
The object travels a distance of 10 km. We need to convert this distance into meters.
- Distance \( d = 10 \text{ km} = 10,000 \text{ m} \)

### Step 2: Calculate Time for First Segment
Now, we calculate the time taken to travel the first 10 km at a speed of 100 m/s.
- Using the formula:
\[ t_1 = \frac{d_1}{v_1} \]
where \( d_1 = 10,000 \text{ m} \) and \( v_1 = 100 \text{ m/s} \):
\[ t_1 = \frac{10,000 \text{ m}}{100 \text{ m/s}} = 100 \text{ seconds} \]

### Step 3: Calculate Time for Second Segment
Next, we calculate the time taken to travel the second 10 km at a speed of 50 m/s.
- Using the formula:
\[ t_2 = \frac{d_2}{v_2} \]
where \( d_2 = 10,000 \text{ m} \) and \( v_2 = 50 \text{ m/s} \):
\[ t_2 = \frac{10,000 \text{ m}}{50 \text{ m/s}} = 200 \text{ seconds} \]

### Step 4: Calculate Total Distance and Total Time
Now, we can find the total distance and total time.
- Total Distance \( D = d_1 + d_2 = 10,000 \text{ m} + 10,000 \text{ m} = 20,000 \text{ m} \)
- Total Time \( T = t_1 + t_2 = 100 \text{ seconds} + 200 \text{ seconds} = 300 \text{ seconds} \)

### Step 5: Calculate Average Speed
Finally, we can calculate the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T} \]
Substituting the values:
\[ \text{Average Speed} = \frac{20,000 \text{ m}}{300 \text{ seconds}} = \frac{200}{3} \text{ m/s} \approx 66.67 \text{ m/s} \]

### Final Answer
The average speed over the whole distance is approximately **66.67 m/s**.

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