Stopping Distance

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 1.19 — Stopping distance as thinking distance plus braking distance
• 1.20 — Factors affecting stopping distance: speed, mass, road condition and reaction time

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

A hazard appears ahead. From that instant to the moment the car is stationary, the car keeps travelling — and the distance it covers is made of two quite separate pieces, produced by two quite different mechanisms. Nearly every mark lost on this topic comes from treating them as one.

The two halves, and where the boundary between them is

1. THINKING DISTANCE. The hazard appears. Your eyes register it, your brain decides, your foot moves to the pedal. Throughout that interval NOTHING has yet acted on the car, so it carries on at its original speed in a straight line — obeying nature, not misbehaving.
2. The boundary is the moment the brakes actually begin to act. Not the moment you decide, and not the moment you move your foot.
3. BRAKING DISTANCE. Now a backward force acts. The car decelerates, and the distance it covers while doing so depends on how fast it was going, how heavy it is, and how big a force the brakes and the road can supply.
4. STOPPING DISTANCE = THINKING DISTANCE + BRAKING DISTANCE. Both are real distances travelled by a real car, and the total is what actually separates you from the hazard.

Thinking distance is the easier of the two to calculate, because during it nothing is changing: the speed is constant, so distance = speed × time. If your reaction time is 0.7 s and you are travelling at 20 m/s, you cover 14 m before the brakes do anything at all. Notice what that expression contains and what it does not. It contains your reaction time and the speed. It does not contain the mass of the car, the condition of the road, or the state of the brakes — none of those can affect a distance covered before any braking has begun. This is the single most examined point on the page.

Think of it like the gap between a shout and the runner turning

Imagine shouting to someone running towards you to stop. There is a delay while the sound reaches them, they register it and begin to slow — and during all of that they keep running at exactly the pace they were running at. Nothing you can do about their shoes, or the surface, or how heavy they are, changes that first stretch: it is set entirely by how fast they were going and how long they took to react. Only after they begin to slow do the shoes and the surface start to matter. The two halves of stopping distance work the same way, which is why a factor has to be assigned to one half or the other before it can be discussed at all.

Braking distance is where everything else acts, and there is one relationship worth understanding rather than memorising. The braking force has to remove all of the car's kinetic energy, and kinetic energy depends on the SQUARE of the speed. So doubling the speed does not double the braking distance — it roughly quadruples it, because there is four times as much kinetic energy to remove with the same force. Thinking distance, by contrast, simply doubles when the speed doubles, because it is a constant-speed distance. The two halves scale differently with speed, and at motorway speeds the braking half dominates the total completely.

The two halves calculated separately, then added

A car travels at 20 m/s. The driver's reaction time is 0.70 s and, once the brakes act, the car decelerates uniformly at 5.0 m/s². Find the total stopping distance.

1. THINKING DISTANCE: the speed is constant during the reaction time, so distance = speed × time.
2. = 20 × 0.70 = 14 m.
3. BRAKING DISTANCE: use v² = u² + 2as with u = 20 m/s, v = 0 (it stops) and a = −5.0 m/s².
4. 0 = 20² + 2 × (−5.0) × s, so 10s = 400 and s = 40 m.
5. STOPPING DISTANCE = 14 + 40 = 54 m.

Answer: 54 m — of which only 40 m involves the brakes at all.

Now the factors, each assigned to the half it acts on. Anything that lengthens the driver's REACTION TIME lengthens the thinking distance only: tiredness, alcohol or drugs, distraction, age and inexperience. Anything that reduces the braking force, or increases what that force has to overcome, lengthens the braking distance only: a wet or icy or greasy ROAD SURFACE, worn tyres, worn brakes, and a greater MASS — a loaded lorry has far more kinetic energy at the same speed. SPEED is the only factor that lengthens both, which is exactly why it appears in every road-safety campaign ever run.

One caution about mass, because the specification names it and the obvious statement is wrong. A heavier vehicle does have more kinetic energy at the same speed, so with the same braking force it takes longer to stop. But it does not think more slowly: mass has no effect whatsoever on thinking distance. An answer that says 'a heavier car has a longer stopping distance because it takes longer to react' is not slightly imprecise, it is describing something that does not happen.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

stopping distance = thinking distance + braking distance

thinking distance is the distance travelled during the driver's reaction time; braking distance is the distance travelled while the braking force acts

Units: All three in metres (m). Thinking distance = speed × reaction time, so m = m/s × s.

Learn this definition · Thinking distance

The distance travelled by the vehicle during the driver's reaction time — from the hazard appearing to the brakes beginning to act. The speed is constant throughout it.

Learn this definition · Braking distance

The distance travelled by the vehicle from the moment the brakes begin to act until it stops.

The two halves, in one line each

A. THINKING DISTANCE: travelled at CONSTANT speed, before the brakes act. Depends on speed and reaction time only.

B. BRAKING DISTANCE: travelled while DECELERATING, after the brakes act. Depends on speed, mass, brakes, tyres and road surface.

Which half does each factor lengthen? — the table the marks come from

Calculating a stopping distance — the routine to follow

1. Find the thinking distance: multiply the speed by the reaction time.
2. Find the braking distance: use v² = u² + 2as, with v = 0 and a negative for a deceleration.
3. Add the two together to get the stopping distance.
4. Check the thinking distance used the ORIGINAL speed, not an average, because the speed is constant during it.

The relationships with speed — worth stating in an explain answer

• THINKING distance is PROPORTIONAL to speed: double the speed and it doubles
• BRAKING distance depends on the SQUARE of the speed: double the speed and it roughly quadruples
• Because kinetic energy depends on speed squared, and all of it must be removed by the braking force
• So at high speed the braking half dominates the total, and speed is the only factor that lengthens both halves

Model answer [3 marks]

A lorry and a car travel at the same speed and brake with the same deceleration. Explain why the lorry's stopping distance is greater. [3]

Both vehicles have the same thinking distance, because the driver's reaction time and the speed are the same and mass has no effect on it. The lorry has a much greater mass, so at the same speed it has much more kinetic energy. All of that kinetic energy must be removed by the braking force, so a greater braking force or a greater distance is needed, and the lorry's braking distance is longer. Since the thinking distances are equal and the braking distance is longer, the lorry's total stopping distance is greater.

Not this: A heavier vehicle has a longer stopping distance because the driver takes longer to react.

This: Mass has no effect at all on reaction time or on thinking distance. It acts entirely on the braking half, because a greater mass means more kinetic energy for the braking force to remove.

Mark-losing trap. Thinking distance depends on SPEED and REACTION TIME only. Not mass, not the road, not the brakes.

Mark-losing trap. Doubling the speed roughly QUADRUPLES the braking distance — kinetic energy goes as speed squared.

Mark-losing trap. The boundary is when the brakes ACT, not when the driver decides or moves their foot.

Mark-losing trap. 'Stopping distance' means the total. Read whether a question wants the total or just one half.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · State [1 mark] — Stopping distance is made up of two parts. Thinking distance is one — what is the other?
2. Grade 7 · Calculate [2 marks] — A car is travelling at 24 m/s. The driver's reaction time is 0.75 s. Calculate the thinking distance.
3. Grade 8 · Explain [5 marks] — A driver has been awake for twenty hours. Select every statement that belongs in a full-mark explanation of how this affects the car's stopping distance.
4. Grade 9 · Calculate [4 marks] — A car travels at 30 m/s. The driver's reaction time is 0.60 s and the car then decelerates uniformly at 7.5 m/s². Calculate the total stopping distance.
5. 9+ · Analyse [6 marks] — A road-safety leaflet claims: 'Cutting your speed from 30 m/s to 15 m/s halves your stopping distance.' Select every statement that belongs in a full-mark analysis of this claim.

The people behind this science

Two ways into the same idea — the one who worked out that moving things need no reason to keep moving, and the one who made the stopping calculable rather than merely describable. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Galileo Galilei — the one who worked out that moving things need no reason to keep moving

The thinking-distance half of this page is a demonstration of the idea Galileo had to fight for. Before him it was taken for granted that a body needs a continuous push to keep moving and stops naturally when the push is removed — on that view a car with no accelerator pressed would slow immediately, and thinking distance would barely exist. Galileo argued from balls rolling down one slope and up another that a body on a level surface, if nothing opposed it, would carry on indefinitely. Those fourteen metres before the brakes bite are that argument, on a road.

• “Why does a moving body keep moving with nothing pushing it?”
• “How did rolling balls down slopes lead you to that conclusion?”
• “What did people believe about moving objects before you argued otherwise?”
• “If nothing opposed a moving body, what would it actually do?”
• “How can friction be studied when you cannot switch it off?”

Isaac Newton — the one who made the stopping calculable rather than merely describable

Galileo established that the car keeps going; Newton supplies the arithmetic of making it stop. His second law says the deceleration a braking force produces is that force divided by the mass, which is precisely why the same brakes take a heavier vehicle further. His first law is the thinking-distance half stated as a principle. The whole page is the first two laws applied to one situation, and separating the two halves is really separating the law that governs each.

• “How does the mass of a vehicle change the effect of a braking force?”
• “What exactly is a force doing when it slows something down?”
• “Why does twice the speed need four times the distance to stop?”
• “Is friction a force in the same sense as a push or a pull?”
• “What would happen to a moving body with no force on it at all?”

Then defend it

On Incandio a lesson is not finished when the questions come out right. You teach the idea back to Ember, an AI apprentice who asks the awkward question, and then you argue it against Émilie du Châtelet in a structured debate marked against descriptors you can read before you enter. Learn it, teach it, then defend it — all three happen on this page once the app loads.

Carry on through the course

• Previous lesson: Weight and Terminal Velocity
• Next lesson: Hooke's Law and Elasticity
• Speed, and What a Distance–Time Graph Is Telling You — Speed as a rate, the units physics insists on, and how to read a journey straight off a graph.
• Acceleration and the Velocity–Time Graph — What acceleration actually measures, why its unit looks strange, and how one graph gives you both acceleration and distance.
• Forces, Vectors and Scalars — What a force actually does, why some quantities need a direction to mean anything, and why that makes a force one of them.
• Resultant Force, Friction and F = ma — Why a moving object stops, what really happens when you add forces up, and the one equation that connects force to motion.
• Weight and Terminal Velocity — What weight actually is, why it is not the same as mass, and what happens to a falling object once the air starts pushing back.
• All of Physics · Incandio Science