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

Options

A. 75 m/s
B. 55 m/s
C. 66.7 m/s
D. 33.3 m/s

Answer

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

### Step 1: Calculate Total Distance
The total distance traveled by the object is the sum of the two distances:
- Distance 1 = 10 km
- Distance 2 = 10 km

Total Distance = Distance 1 + Distance 2 = 10 km + 10 km = 20 km

### Step 2: Calculate Time Taken for Each Segment
To find the average speed, we need to calculate the time taken for each segment of the journey.

**For the first segment:**
- Distance = 10 km
- Speed = 100 km/s

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Time for the first segment (t1):
\[ t_1 = \frac{10 \text{ km}}{100 \text{ km/s}} = \frac{10}{100} \text{ s} = 0.1 \text{ s} \]

**For the second segment:**
- Distance = 10 km
- Speed = 50 km/s

Time for the second segment (t2):
\[ t_2 = \frac{10 \text{ km}}{50 \text{ km/s}} = \frac{10}{50} \text{ s} = 0.2 \text{ s} \]

### Step 3: Calculate Total Time
Now, we can find the total time taken for the entire journey:
\[ \text{Total Time} = t_1 + t_2 = 0.1 \text{ s} + 0.2 \text{ s} = 0.3 \text{ s} \]

### Step 4: Calculate Average Speed
Now, we can use the average speed formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values:
\[ \text{Average Speed} = \frac{20 \text{ km}}{0.3 \text{ s}} \]

To convert km to m, we use the conversion factor (1 km = 1000 m):
\[ \text{Average Speed} = \frac{20,000 \text{ m}}{0.3 \text{ s}} = 66,666.67 \text{ m/s} \]

Converting back to km/s:
\[ \text{Average Speed} \approx 66.67 \text{ km/s} \]

### Conclusion
The average speed over the whole distance is approximately **66.67 km/s**.

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