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:-

Explanation

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

### Step 1: Determine the total distance traveled
The object travels two segments:
- First segment: 10 km
- Second segment: 10 km

**Total distance (D)** = 10 km + 10 km = 20 km

### Step 2: Convert the total distance to meters
Since the speeds are given in meters per second, we should convert kilometers to meters.
1 km = 1000 meters, so:
**Total distance (D)** = 20 km × 1000 m/km = 20000 m

### Step 3: Calculate the time taken for each segment
1. For the first segment (10 km at 100 m/s):
- Distance = 10 km = 10000 m
- Speed = 100 m/s
- Time (t1) = Distance / Speed = 10000 m / 100 m/s = 100 seconds

2. For the second segment (10 km at 50 m/s):
- Distance = 10 km = 10000 m
- Speed = 50 m/s
- Time (t2) = Distance / Speed = 10000 m / 50 m/s = 200 seconds

### Step 4: Calculate the total time taken
**Total time (T)** = Time for first segment + Time for second segment
T = t1 + t2 = 100 seconds + 200 seconds = 300 seconds

### Step 5: Calculate the average speed
Average speed (V_avg) is defined as total distance divided by total time:
\[ V_{avg} = \frac{D}{T} \]
\[ V_{avg} = \frac{20000 \text{ m}}{300 \text{ s}} \]

### Step 6: Simplify the average speed calculation
\[ V_{avg} = \frac{20000}{300} = \frac{200}{3} \approx 66.67 \text{ m/s} \]

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

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