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The image shows a problem related to the stopping distances of a vehicle at different speeds. The problem is written in German and seems to involve calculating the braking distance and total stopping distance based on various speeds.

### Translation and Breakdown:

**Aufgabe 50 (9.7)**
- The task is to analyze the stopping distances depending on different speeds. It asks to determine the total stopping distance based on reaction distance (Reaktionsweg) and braking distance (Bremsweg).

### Speeds and Distances:
- **a) 30 km/h** 
  - Reaction distance: 9 meters
  - Braking distance: 4.5 meters
  - Total stopping distance: 13.5 meters

- **b) 50 km/h**
  - Reaction distance: 15 meters
  - Braking distance: 12.5 meters
  - Total stopping distance: 27.5 meters

- **c) 100 km/h**
  - Reaction distance: 30 meters
  - Braking distance: 50 meters
  - Total stopping distance: 80 meters

- **d) 120 km/h**
  - Reaction distance: 36 meters
  - Braking distance: 72 meters
  - Total stopping distance: 108 meters

### Explanation:
- The **reaction distance** depends linearly on the speed because it is the distance covered during the driver's reaction time.
- The **braking distance** increases with the square of the speed, which means that as the speed doubles, the braking distance quadruples.
- The **total stopping distance** is the sum of the reaction distance and the braking distance.

Would you like to dive into the detailed calculations or explore related questions? Here are five related questions for further study:

1. How is the braking distance formula derived, and why does it depend on the square of the speed?
2. What factors can affect the reaction time and braking efficiency?
3. How would the stopping distances change in adverse weather conditions like rain or snow?
4. Can you calculate the stopping distance for a speed not listed here, such as 80 km/h?
5. How does the mass of a vehicle influence the braking distance?

**Tip:** Always keep in mind that stopping distances are crucial for road safety, especially at higher speeds. Regularly reviewing the impact of speed on stopping distances can enhance driving awareness.

Analyze the stopping distances depending on different speeds, determining the total stopping distance based on reaction distance (Reaktionsweg) and braking distance (Bremsweg).

This problem explains how to calculate the total stopping distance for different vehicle speeds, taking into account the reaction distance and braking distance. Explore the impact of speed on stopping distances with examples at 30 km/h, 50 km/h, 100 km/h, and 120 km/h. Ideal for students in Grades 10-12.

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