8.1.6Global Challenges
Estimating Braking Distances, Speeds and Accelerations
5 min read 6 parts Lesson 7 of 21 Unit quiz
Section 1 of 6Stopping Distance
The total distance needed to stop has two separate parts.
Thinking distance
- The distance travelled during the driver's reaction time, found from speed × reaction time at constant speed.
Braking distance
- The distance travelled after the brakes are applied until the vehicle is at rest.
Total
- Stopping distance equals thinking distance plus braking distance.
Typical reaction time
- A normal reaction time is about 0.2 to 0.9 seconds, and tiredness, alcohol or distraction makes it longer.
Section 2 of 6Calculating with v² = u² + 2as
For a car braking at constant deceleration, follow these steps.
1
Convert the speed to metres per second, because the equation only works in SI units.
2
Set the final velocity v to zero, since the vehicle ends at rest.
3
Rearrange the equation to give the braking distance s = u² ÷ (2a), using the size of the deceleration.
4
Work out the thinking distance separately as speed multiplied by reaction time.
5
Add the two distances and give the answer with a sensible number of significant figures.
Section 3 of 6Effect of Speed
Effect of Speed
Thinking distance
- This is directly proportional to speed, so doubling the speed doubles the thinking distance.
Braking distance
- This is proportional to the speed squared, so doubling the speed makes it four times longer.
Road conditions
- Wet or icy roads and worn tyres reduce the possible deceleration, which increases braking distance.
Why it matters
- Small increases in speed raise stopping distance greatly, which is why speed limits are lower near schools.
| Speed (m/s) | Thinking distance (m) | Braking distance (m) | Stopping distance (m) |
|---|---|---|---|
| 10 | 7 | 10 | 17 |
| 20 | 14 | 40 | 54 |
| 30 | 21 | 90 | 111 |
Section 4 of 6Typical Values to Remember
The table above uses a reaction time of 0.7 s and a deceleration of 5 m/s².
Walking and cycling
- A person walks at about 1.5 m/s and cycles at about 6 m/s, which helps judge whether an estimate is reasonable.
Car speeds
- A car on a motorway travels at roughly 30 m/s, which is about 70 mph.
Car acceleration
- A family car accelerating from rest reaches 27 m/s in about 10 seconds, an acceleration near 2.7 m/s².
Checking answers
- A braking distance of several kilometres, or a deceleration far above 10 m/s², should alert you to an error.
Section 5 of 6Worked Example
Question
- A car travels at 25 m/s.
- The driver's reaction time is 0.80 s and the car then decelerates uniformly at 6.0 m/s².
- Calculate the stopping distance.
- Thinking distance = 25 × 0.80 = 20 m.
- Braking distance0 = 25² − 2 × 6.0 × s, so s = 625 ÷ 12 = 52.1 m.
- Stopping distance = 20 + 52.1 = 72.1 m.
Answer The stopping distance is about 72 m.
Section 6 of 6Exam Checklist & Tips
8.1.6 – Key Points for the Exam
- Thinking distance The distance a vehicle travels while the driver reacts to a hazard.
- Braking distance The distance a vehicle travels while the brakes are slowing it to a stop.
- Stopping distance The sum of thinking distance and braking distance.
- Reaction time The time between seeing a hazard and starting to brake.
- Uniform acceleration Acceleration that stays constant, so the equations of motion can be used.
Common Mistakes
- Using the equation v² = u² + 2as with speed in km/h rather than m/s.
- Treating braking distance as proportional to speed instead of speed squared.
- Forgetting to add the thinking distance to the braking distance.
- Using a negative acceleration and a negative distance together and losing track of the sign.