Edexcel IGCSE Physics · Spec 1.9
Stopping Distances
Thinking distance, braking distance, and the factors affecting stopping distance.
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Stopping Distances
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Explained
Stopping distance, and why it splits into two halves
Stopping distance is the total distance a vehicle travels from the moment the driver sees a hazard to the moment the vehicle stops. It is made of two parts, and almost every question here depends on keeping them apart.
Thinking distance is the distance travelled while the driver reacts, between seeing the hazard and pressing the brake. During it the vehicle is still going at full speed, because nothing has happened to it yet.
Braking distance is the distance travelled once the brakes are applied, while the vehicle slows to a stop.
Stopping distance is the two added together. That is the definition, and it is worth writing as an equation because questions often give you two of the three values.
What changes each one
The two halves have almost entirely separate causes, which is the point of the split.
Thinking distance depends on the driver, because it depends on reaction time. Tiredness, alcohol, drugs, distraction such as a phone, and simple inexperience all lengthen it. Nothing about the car or the road makes any difference to it at all.
Braking distance depends on the vehicle and the road. Worn brakes, worn or under inflated tyres, a heavier load, and a wet, icy or gravelled surface all lengthen it. A tired driver brakes just as effectively as a fresh one once the pedal is down.
Speed is the exception, and that is why it matters more than anything else on this page. Speed increases both. It increases thinking distance, because you cover more ground in the same reaction time, and it increases braking distance, because there is more kinetic energy to remove.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme sets three short questions on this in sequence, and prints its reasoning for every wrong option.
The first defines thinking distance as the distance travelled between seeing the obstacle and applying the brakes. Its rejections are precise: one option is the braking distance, another is the stopping distance, and a third is only part of the braking distance.
The second asks which factor increases the braking distance, and the answer is worn tyres on the car. Its notes explain each of the others in one line each. Two of them would decrease the braking distance. The remaining one increases the thinking distance, so it is a real effect on stopping but on the wrong half of it.
That is the trap, and it is set deliberately. A distractor here is not nonsense; it is a genuine factor filed under the wrong heading. Before answering, decide which half of the stopping distance the question is about, then ask whether the factor is about the driver or about the vehicle and the road.
The third question asks which quantity affects both, and the answer is the speed of the car, with velocity allowed. One mark, and it is the whole reason speed limits exist.
Why speed matters more than it looks
Thinking distance is proportional to speed. Double the speed and you cover twice as much ground in the same reaction time.
Braking distance is proportional to the square of the speed. Double the speed and the braking distance is four times as long, because kinetic energy depends on velocity squared and all of it has to be transferred away by the brakes.
So doubling the speed does not double the stopping distance. It roughly triples it, because one part doubles and the other quadruples. That is the argument behind lower limits outside schools, and it is a calculation you can be asked to do.
Answering with energy
The work done by the braking force equals the kinetic energy the vehicle had, so braking force multiplied by braking distance equals one half m v squared.
Rearranged, the braking distance is the kinetic energy divided by the braking force. That single expression explains every factor in the list: more mass or more speed means more kinetic energy on top, and worn brakes or a slippery road means a smaller force underneath.
It also explains why hard braking heats the brake discs. The kinetic energy has not disappeared; it has been transferred to the thermal store of the brakes and the surroundings by the friction between the pads and the discs.
Reading it off a graph
On a velocity time graph, the thinking distance is the area of the rectangle where the velocity is constant, and the braking distance is the area of the triangle where it falls to zero.
The total area under the graph is the stopping distance. Splitting the shape into a rectangle and a triangle is not a trick for finding an area; it is the two halves of the definition drawn out.
Spec 1.9
What you need to know
- Define thinking, braking and stopping distance
- List what affects each one
- Link stopping distance to road safety
Active recall
Quick check
Answer each question before opening the answer.
What two distances add together to give the stopping distance?
Thinking distance + braking distance.
Give two factors that increase the braking distance.
Any two of: higher speed, wet or icy roads, worn tyres or brakes, greater mass.
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