💤 Tiredness
A tired driver is less alert and takes longer to notice a hazard and respond to it.
Forces, Movement, Shape and Momentum » Stopping Distances
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.19, 1.20
- That stopping distance is the thinking distance added to the braking distance
- Which factors change the thinking distance and which change the braking distance
- How to calculate a thinking distance from speed and reaction time
- Why the braking distance grows much faster than the speed
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Unlock This CourseWhat is stopping distance?
A driver sees a ball bounce into the road ahead. The car does not stop straight away. Stopping happens in two stages.
First, the driver has to notice the danger and move a foot onto the brake pedal. This takes a short time, and the car carries on at its full speed while it happens. Second, the brakes are on and the car slows down until it is at rest.
Each stage covers some distance along the road. Add the two distances together and you get the total distance the car needs to stop:
stopping distance = thinking distance + braking distance
Key terms:
- Thinking distance: the distance a vehicle travels during the driver's reaction time, before the brakes are applied.
- Braking distance: the distance a vehicle travels from the moment the brakes are applied until it stops.
- Stopping distance: the total distance a vehicle travels from the moment the driver sees a hazard until it stops. It is the sum of the thinking distance and the braking distance.
Thinking distance
Remember, reaction time is the time a person takes to respond to something they see or hear. For an alert driver it is usually less than one second. During this time the driver has not yet pressed the brake, so the vehicle keeps moving at a constant speed. That means you can use the average speed equation, rearranged to give distance:
thinking distance = speed × reaction time
Use the speed in m/s and the reaction time in s to get the thinking distance in m. The equation shows that only two things can change the thinking distance: the speed of the vehicle and the reaction time of the driver.
Worked example 1: finding a thinking distance
A car travels through a town at 12 m/s. The driver has a reaction time of 0.5 s. Calculate the thinking distance.
thinking distance = speed × reaction time
thinking distance = 12 × 0.5
thinking distance = 6 m
Worked example 2: a higher speed
The same driver travels along a motorway at 30 m/s. The reaction time is still 0.5 s. Calculate the thinking distance.
thinking distance = 30 × 0.5
thinking distance = 15 m
The car covers more distance each second, so it travels further before the driver has even touched the brake. Thinking distance is directly proportional to speed: double the speed and the thinking distance doubles.
Worked example 3: finding a reaction time
A van travels at 24 m/s. Its thinking distance is 36 m. Calculate the reaction time of the driver.
reaction time = thinking distance / speed
reaction time = 36 / 24
reaction time = 1.5 s
This is a slow reaction time. The driver may be tired or distracted.
What makes reaction time longer?
Anything that slows the driver's reactions makes the reaction time longer. A longer reaction time means a longer thinking distance, and so a longer stopping distance.
🍺 Alcohol
Alcohol slows down the driver's reactions, even in small amounts.
💊 Drugs
Illegal drugs and some medicines slow the driver's reactions.
📱 Distractions
A driver who is using a mobile phone, or talking to passengers, is not giving the road their full attention and takes longer to notice the hazard and react.
None of these change the braking distance. Once the brakes are on, the driver's reaction time no longer matters.
Braking distance
The brakes and the friction between the tyres and the road provide the force that slows the vehicle down. The braking distance depends on the vehicle and the road, not on the driver's reactions.
💨 Speed
A faster vehicle has more speed to lose, so it travels much further while it slows to a stop.
🚛 Mass
Remember F = m × a. With the same braking force, a vehicle with a bigger mass has a smaller deceleration, so it takes a longer distance to stop. A fully loaded lorry needs more road than an empty one.
☔ Road condition
On a wet or icy road there is less friction between the tyres and the road. The force slowing the vehicle is smaller, so the braking distance is longer.
The condition of the vehicle matters as well. Worn tyres have less grip on the road, mainly when it is wet. Worn brakes cannot give as large a braking force. Both make the braking distance longer.
Which factor changes which distance?
| Factor | Thinking distance | Braking distance |
|---|---|---|
| Higher speed | Longer | Longer |
| Longer reaction time (tiredness, alcohol, drugs, distractions) | Longer | No change |
| Bigger mass | No change | Longer |
| Wet or icy road | No change | Longer |
| Worn tyres or worn brakes | No change | Longer |
Speed is the only factor in both columns. That is why speed has such a big effect on the stopping distance.
Speed and braking distance
Thinking distance goes up in step with speed. Braking distance does not. It rises much faster than the speed. The table shows typical values for a car on a dry road with good brakes and tyres, taken from the Highway Code.
| Speed in mph | Thinking distance in m | Braking distance in m | Stopping distance in m |
|---|---|---|---|
| 20 | 6 | 6 | 12 |
| 40 | 12 | 24 | 36 |
| 60 | 18 | 55 | 73 |
Look at what happens when the speed doubles from 20 mph to 40 mph. The thinking distance doubles, from 6 m to 12 m. The braking distance becomes four times as long, from 6 m to 24 m. At three times the speed, the braking distance is about nine times as long. You do not need to calculate braking distances in this lesson, but you do need to describe this pattern.
Describing the graphs. If you plot thinking distance (up the side) against speed (along the bottom), you get a straight line through the origin. If you plot braking distance against speed, you get a curve that starts at the origin and gets steeper and steeper as the speed increases.
Worked example 4: finding a stopping distance
A motorcyclist rides at 20 m/s. Her reaction time is 0.6 s. The braking distance at this speed is 32 m. Calculate the stopping distance.
thinking distance = speed × reaction time = 20 × 0.6 = 12 m
stopping distance = thinking distance + braking distance
stopping distance = 12 + 32
stopping distance = 44 m
Common mistakes
- Mixing up the two distances. Things that affect the driver (tiredness, alcohol, drugs, distractions) change the thinking distance. Things that affect the vehicle or the road (mass, brakes, tyres, water, ice) change the braking distance.
- Saying that a wet road increases the thinking distance. The driver reacts just as quickly in the rain. It is the braking distance that gets longer.
- Forgetting that speed affects both. A higher speed makes the thinking distance and the braking distance longer.
- Writing "thinking time" when you mean thinking distance. Reaction time is in seconds. Thinking distance is in metres.
- Saying the braking distance doubles when the speed doubles. It becomes about four times as long.
Exam-style question
A car travels along a dry road at 24 m/s. The driver sees a fallen tree ahead and brakes. The driver's reaction time is 0.5 s.
(a) State what is meant by the term thinking distance. [1 mark]
(b) Calculate the thinking distance of the car. [2 marks]
(c) The braking distance of the car is 48 m. Calculate the stopping distance. [1 mark]
(d) On another day the driver makes the same journey at the same speed, but the road is wet and the driver is tired. Explain how each of these changes affects the stopping distance of the car. [4 marks]
Model answer
(a) The distance the car travels during the driver's reaction time, before the brakes are applied. (1)
(b) thinking distance = speed × reaction time = 24 × 0.5 (1)
thinking distance = 12 m (1)
(c) stopping distance = 12 + 48 = 60 m (1)
(d) The wet road gives less friction between the tyres and the road (1) so the braking distance is longer (1). Being tired makes the driver's reaction time longer (1) so the thinking distance is longer (1). Both changes make the stopping distance longer.
Exam tip
In a question like part (d), never just write "the stopping distance increases". Say which of the two distances changes, thinking or braking, and give the reason. Here that means linking the wet road to friction and braking distance, and linking tiredness to reaction time and thinking distance.