Stopping Distances
In this lesson we learn about typical stopping distances.
IN THIS LESSON:
Typical stopping distances
Expected distances
How velocity affects typical stopping distances
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Practice Questions
Introduction: Stopping Distances
The total stopping distance of a car is a critical measure for road safety. The following table shows typical stopping distances in the UK under good conditions (dry road, good tyres, alert driver). These values are vital for understanding why speed limits are set as they are.
| Speed | Total Stopping Distance | Thinking Distance | Braking Distance |
|---|---|---|---|
| 20 mph | 12 m | 6 m | 6 m |
| 30 mph | 23 m | 9 m | 14 m |
| 40 mph | 36 m | 12 m | 24 m |
| 50 mph | 53 m | 15 m | 38 m |
| 60 mph | 73 m | 18 m | 55 m |
| 70 mph | 96 m | 21 m | 75 m |
Note: These distances are based on the UK Highway Code and are under ideal conditions. Real-world distances can be much greater.
Question 1: According to the table, what is the typical total stopping distance for a car travelling at 30 mph?
Answer: The typical total stopping distance at 30 mph is 23 m.
Question 2: A car is travelling at the maximum speed limit on a motorway in good conditions. What is its typical thinking distance and braking distance?
Answer: The maximum speed limit on a motorway in the UK is 70 mph.
- Thinking distance: 21 m
- Braking distance: 75 m
Question 3: Describe the pattern you can see in the thinking distance as the speed increases.
Answer: As the speed increases, the thinking distance also increases. For every 10 mph increase in speed, the thinking distance increases by roughly 3 m. This shows a linear or directly proportional relationship between speed and thinking distance.
Question 4: Describe the pattern you can see in the braking distance as the speed increases.
Answer: As the speed increases, the braking distance increases much more rapidly. The braking distance grows much faster than the thinking distance, which shows a non-linear relationship, specifically a squared relationship with speed. For example, doubling the speed from 30 mph to 60 mph increases the braking distance from 14 m to 55 m, which is nearly a factor of four.
Question 5: Calculate the typical reaction time of the driver based on the data in the table. Use the data for a speed of 30 mph.
Answer Walkthrough:
- Given: Speed (v) = 30 mph = 13.4 m/s (approx.), Thinking distance (dthinking) = 9 m.
- Formula: Time = Distance / Speed
- Calculation: Time = 9 m / 13.4 m/s ≈ 0.67 s.
Answer: The typical reaction time is approximately 0.67 s.
Question 6: A driver sees a hazard 50 m ahead while driving at 50 mph. Using the table, explain whether the driver will be able to stop in time under ideal conditions.
Answer: No, the driver will likely not stop in time. The total stopping distance for a car travelling at 50 mph is 53 m under ideal conditions, which is greater than the 50 m distance to the hazard.
Question 7: Compare the total stopping distance at 40 mph with the total stopping distance at 20 mph.
Answer:
- At 20 mph, the total stopping distance is 12 m.
- At 40 mph, the total stopping distance is 36 m.
The stopping distance at 40 mph is three times greater than at 20 mph.
Question 8: A driver is travelling at 30 mph in a residential area. A child runs into the road 15 m in front of the car. Using the data, explain what happens to the child.
Answer: At 30 mph, the car's thinking distance alone is 9 m. This means the car travels 9 m before the brakes are even applied. This leaves only 6 m of braking distance to stop before reaching the child. Since the braking distance at this speed is 14 m, the car will not stop in time and will hit the child.
Question 9: The speed limit on a typical residential road is 30 mph. Based on the stopping distance data, explain why this limit is important for pedestrian safety.
Answer: At 30 mph, the total stopping distance is 23 m. This distance is manageable in a residential area, giving the driver a chance to stop if a person or obstacle appears. If the speed were much higher, like 50 mph (with a stopping distance of 53 m), the stopping distance would be too long to prevent collisions with people who might unexpectedly step into the road. The low speed limit is set to make stopping distances shorter and manageable for the environment.
Question 10: A car is travelling at 70 mph. What percentage of the total stopping distance is made up by the braking distance?
Answer Walkthrough:
- Given: Total distance = 96 m, Braking distance = 75 m.
- Formula: Percentage = (Part / Whole) x 100
- Calculation: Percentage = (75 m / 96 m) x 100 ≈ 78.1%.
Answer: The braking distance makes up approximately 78% of the total stopping distance at 70 mph.
Question 11: Explain why the braking distance makes up a larger proportion of the total stopping distance at higher speeds.
Answer: Braking distance is proportional to the square of the speed, while thinking distance is only directly proportional to speed. This means that as speed increases, the braking distance increases at a much faster rate than the thinking distance, so it quickly becomes the dominant component of the total stopping distance.
Question 12: A car's braking distance at 50 mph is 38 m. If the road is wet, this distance could increase by 50%. Calculate the new braking distance on a wet road.
Answer Walkthrough:
- Given: Original braking distance = 38 m, Increase = 50%.
- Calculation: Increase = 0.50 × 38 m = 19 m.
- New distance: 38 m + 19 m = 57 m.
Answer: The new braking distance on a wet road is 57 m.
Question 13: In a 30 mph zone, a driver's thinking distance is found to be 15 m instead of the typical 9 m. Suggest a possible reason for this difference.
Answer: A thinking distance of 15 m is significantly longer than typical. This suggests the driver has a much slower reaction time, possibly due to being tired, distracted, or under the influence of alcohol or drugs.
Question 14: A car's total stopping distance is 73 m. What two speeds could the car be travelling at to achieve this distance in ideal conditions? Use the data from the table.
Answer: Based on the table, the car could be travelling at 60 mph.
Question 15: Imagine a new speed limit is introduced for a school zone: 10 mph. Based on the principles of stopping distance, explain why this would be a safer limit than 20 mph for that area.
Answer: At 20 mph, the total stopping distance is 12 m. At 10 mph, the speed is halved, so the thinking distance will be halved (to 3 m), and the braking distance will be a quarter of the original (6 m / 4 = 1.5 m). This gives a total stopping distance of only 4.5 m. This is a significantly shorter distance, making it much easier to stop for a child who might step out, thereby greatly increasing safety.