Speed, Reaction Time and Stopping Distances

Imagine you are driving along a road when, without warning, a ball bounces out between two parked cars and a child chases after it. However quick you are, you cannot stop the car instantly. First there is a brief pause while your eyes register the danger and your foot moves to the brake pedal; only then do the brakes begin to slow the car down. The total distance the car travels from the instant you first spot the hazard to the instant it finally halts is called the stopping distance, and knowing what makes it longer or shorter is genuinely a matter of life and death. This lesson opens the "Physics on the move" part of Topic P6 (Global challenges) of OCR Gateway Combined Science A by splitting the stopping distance into its two parts, examining the factors that stretch each one, and explaining why braking distance grows so steeply as a car goes faster.

By the end of this lesson you should be able to recall some typical everyday speeds, explain that stopping distance is the sum of thinking distance and braking distance, list and explain the factors that affect each part, describe the energy transfer that happens when a car brakes, and explain why doubling the speed makes the braking distance roughly four times as long.

This lesson combines AO1 (recalling typical speeds and the parts of stopping distance) with AO2 (calculating stopping distances and reasoning about the squared speed–braking-distance relationship) and AO3 (interpreting stopping-distance data and factors).

Some Typical Speeds

Before looking at stopping, it is worth having a rough feel for how fast everyday things actually move, because exam questions often expect you to judge whether a speed is sensible. Speeds are measured in metres per second (m/s), and the values below are approximate — nobody walks or runs at exactly the same pace — but they are the right sort of size to remember.

Motion	Typical speed
Walking	about $1.5 \text{ m/s}$
Running	about $3 \text{ m/s}$
Cycling	about $6 \text{ m/s}$
A car in a town (about 30 mph)	about $13 \text{ m/s}$
A car on a motorway (about 70 mph)	about $31 \text{ m/s}$
A commuter train	about $55 \text{ m/s}$

The exact numbers are not something to memorise to the last digit, but you should be able to say that a person walks at "a couple of metres per second" and that a motorway speed is "about thirty metres per second". Wind speeds and the speed of sound (around $330 \text{ m/s}$ in air) are also worth a rough sense of scale.

Exam Tip: If a question gives a speed and asks whether it is reasonable, compare it with these everyday values. A "car" travelling at $3 \text{ m/s}$ is crawling (walking pace), while a person "running" at $30 \text{ m/s}$ is impossible — sanity-checking a number against a typical speed can save you from a silly answer.

Stopping Distance = Thinking Distance + Braking Distance

The total stopping distance of a vehicle is made of two separate distances added together:

$\text{stopping distance} = \text{thinking distance} + \text{braking distance}$

Thinking distance is how far the vehicle travels during the driver's reaction time — the short gap between seeing the hazard and actually pressing the brake pedal. Throughout this time the car keeps moving at its full speed, because the brakes have not yet been touched.
Braking distance is how far the vehicle travels once the brakes are being applied, from the moment the brakes begin to act until the car comes to a complete stop.

Both distances are measured in metres. The stopping distance matters because it tells a driver how much clear road they need ahead of them to be able to pull up safely — which is exactly why the Highway Code insists on keeping a safe following distance.

Exam Tip: Learn the word equation exactly: stopping distance = thinking distance + braking distance. A very common slip is to give only the braking distance when the question asks for the stopping distance — you must remember to add the thinking distance as well.

Factors Affecting Thinking Distance

The thinking distance depends on just two things: how fast the car is moving and the driver's reaction time.

Speed. During the reaction time the car carries on at a steady speed, so the faster it is going the further it travels before the driver even touches the brake. Thinking distance is directly proportional to speed: double the speed and the thinking distance doubles.

Reaction time. Anything that slows the driver's reactions lengthens the thinking distance. Reaction time is increased by:

Tiredness — a tired driver reacts more slowly;
Alcohol — it slows down the nervous system and clouds judgement;
Drugs — both illegal drugs and some prescription or over-the-counter medicines slow reactions;
Distractions — using a phone, adjusting the radio or chatting to passengers all mean the hazard is noticed later.

A typical reaction time for an alert, sober driver is around $0.7 \text{ s}$ , but it can easily double, or worse, if the driver is impaired or distracted.

Exam Tip: All the factors that change thinking distance act on the driver (reaction time) or on the speed. Do not muddle them with the road-and-vehicle factors that change braking distance — examiners give marks for putting each factor in the correct box.

Factors Affecting Braking Distance

The braking distance depends on the speed of the car, its mass, and the braking force available — which itself depends on the condition of the road, the tyres and the brakes.

Speed. The faster the car is going, the greater the braking distance — and, as we shall see, this is not a simple doubling: braking distance grows with the square of the speed.

Mass. A more heavily loaded vehicle has more kinetic energy at a given speed, so the brakes have to do more work to stop it and the braking distance increases.

Road conditions. A wet or icy road, or one covered in leaves, oil or loose gravel, reduces the friction (grip) between the tyres and the road. Less grip means a smaller braking force, so the braking distance increases.

Tyre condition. Worn or bald tyres — especially with too little tread to clear water — grip the road less well, lengthening the braking distance. Correctly inflated tyres with plenty of tread give the best grip.

Brake condition. Worn brake pads, or brakes that have overheated ("brake fade"), provide a smaller braking force, again increasing the braking distance.

Exam Tip: Braking-distance factors act on the vehicle and the road (mass, brakes, tyres, road surface, speed). If a factor changes the grip or the braking force, it changes the braking distance — not the thinking distance.

Energy Transfer When a Car Brakes

To stop a moving car you have to get rid of its kinetic energy — the energy it has because it is moving. That energy does not simply vanish; it is transferred to another store.

When the brakes are applied, the brake pads are squeezed hard against a disc attached to each wheel. As the disc turns against the pads, friction between them does work, and this friction transfers the car's kinetic energy into the thermal (internal) energy store of the brakes, which get hot. In a hard stop from motorway speed the brake discs can reach several hundred degrees Celsius.

We can write the transfer as:

$\text{kinetic energy of car} \longrightarrow \text{thermal energy of brakes (by friction)}$

The greater the speed, the more kinetic energy has to be removed, and the more work the brakes must do — which is exactly why higher speeds mean longer braking distances. If the brakes get too hot they can no longer transfer energy well (brake fade), which is why lorries descending long hills change to a lower gear to help slow down without overheating the brakes.

Exam Tip: Say kinetic energy is transferred to thermal energy in the brakes by friction. Naming the mechanism (friction) and the destination (the thermal store of the brakes) is what earns full marks — "the energy is lost" is not enough.

Why Braking Distance Grows with the Square of the Speed

This is the single most important idea in the topic, and examiners love it. The kinetic energy of a moving car is given by:

$E_k = \dfrac{1}{2}mv^2$

where $m$ is the mass and $v$ is the speed. The key feature is the $v^2$ : kinetic energy depends on the square of the speed.

When a car brakes to a stop, the braking force does work to remove all of that kinetic energy. The work done by the braking force is $W = F \times d$ , where $F$ is the braking force and $d$ is the braking distance. Setting the work done equal to the kinetic energy removed:

$F \times d = \dfrac{1}{2}mv^2$

Rearranging for the braking distance:

$d = \dfrac{mv^2}{2F}$

For a given car and a given braking force, everything except $v^2$ stays the same, so the braking distance is proportional to the speed squared, $d \propto v^2$ . This has a dramatic consequence:

Double the speed ( $v \to 2v$ ) and the braking distance becomes $2^2 = 4$ times as long.
Triple the speed ( $v \to 3v$ ) and the braking distance becomes $3^2 = 9$ times as long.

Worked Example 1 — The effect of doubling speed

A car has a braking distance of $12 \text{ m}$ when travelling at $10 \text{ m/s}$ . Estimate its braking distance at $20 \text{ m/s}$ , assuming the same braking force.

Step 1 — the speed has doubled, from $10 \text{ m/s}$ to $20 \text{ m/s}$ , so the ratio of speeds is $2$ .

Step 2 — braking distance is proportional to speed squared, so multiply the distance by $2^2 = 4$ .

Step 3 — calculate: $12 \times 4 = 48 \text{ m}$ .

Answer: the braking distance is about $48 \text{ m}$ — four times as far.

Worked Example 2 — Using the kinetic energy directly

A car of mass $1200 \text{ kg}$ travels at $15 \text{ m/s}$ . The brakes provide a constant force of $6000 \text{ N}$ . Calculate the braking distance.

Step 1 — find the kinetic energy: $E_k = \dfrac{1}{2}mv^2 = \dfrac{1}{2} \times 1200 \times 15^2$ .

Step 2 — evaluate: $E_k = 0.5 \times 1200 \times 225 = 135\,000 \text{ J}$ .

Step 3 — the braking force does this much work: $F \times d = E_k$ , so $d = \dfrac{E_k}{F} = \dfrac{135\,000}{6000}$ .

Step 4 — calculate: $d = 22.5 \text{ m}$ .

Answer: the braking distance is $22.5 \text{ m}$ .

Exam Tip: If a question doubles or triples the speed and asks about braking distance, use $d \propto v^2$ : multiply the distance by the square of the speed ratio, not just the ratio. This is the classic trap, and marks are routinely thrown away by writing "twice as far" instead of "four times as far".

Typical Stopping Distances

The chart below shows how thinking distance and braking distance combine at three different speeds. Notice that the thinking distance (in blue) grows steadily in proportion to speed, while the braking distance (in orange) grows far more quickly because of the $v^2$ effect.

The table gives approximate figures. The exact numbers are not something you must learn by heart, but the pattern — that braking distance rises far more steeply than thinking distance as the speed increases — is examinable.

Speed	Thinking distance	Braking distance	Stopping distance
$13 \text{ m/s}$ (about 30 mph)	$9 \text{ m}$	$14 \text{ m}$	$23 \text{ m}$
$22 \text{ m/s}$ (about 50 mph)	$15 \text{ m}$	$38 \text{ m}$	$53 \text{ m}$
$31 \text{ m/s}$ (about 70 mph)	$21 \text{ m}$	$75 \text{ m}$	$96 \text{ m}$

Exam Tip: In a data question, remember thinking distance is proportional to speed (roughly doubles when the speed doubles) but braking distance is proportional to speed squared (roughly quadruples). Comparing the two columns is a classic extended-response question.

Common Misconceptions

Misconception	The correct idea
"Stopping distance is just the braking distance"	Stopping distance = thinking distance + braking distance — you must include the thinking distance
"Doubling the speed doubles the braking distance"	Braking distance is proportional to speed squared, so doubling the speed makes it about four times as long
"Alcohol increases the braking distance"	Alcohol slows reactions, so it increases the thinking distance; it does not change the braking force
"Worn tyres increase the thinking distance"	Worn tyres reduce grip, increasing the braking distance; they have no effect on reaction time
"The lost kinetic energy just disappears"	It is transferred to the thermal store of the brakes by friction — the brakes get hot
"A heavier car and a lighter car have the same braking distance"	A heavier car has more kinetic energy, so its braking distance is greater for the same braking force

Model Answer — Explaining Braking Distance and Speed

Question (6 marks): A driver is travelling at $30 \text{ m/s}$ instead of $15 \text{ m/s}$ . Explain, in terms of energy, why the braking distance is much greater at the higher speed, and describe what happens to the car's kinetic energy when it brakes.

Mid-band response: "The car is going faster so it has more energy and takes longer to stop. When it brakes the energy goes into the brakes and they get hot."

Examiner-style commentary: The response has the right ideas — more speed means more energy and a longer stop, and the energy goes to the brakes — but it is vague. There is no mention of kinetic energy, no use of the $v^2$ relationship, and "takes longer to stop" confuses time with distance. To improve, name the kinetic energy store, quote $E_k = \dfrac{1}{2}mv^2$ , and use the square relationship.

Stronger response: "The kinetic energy of the car is $E_k = \dfrac{1}{2}mv^2$ . Because it depends on $v^2$ , doubling the speed makes the kinetic energy four times as big. When the brakes are applied, the braking force does work to remove this energy, so a bigger braking distance is needed. The kinetic energy is transferred to thermal energy in the brakes."

Examiner-style commentary: A good answer that quotes the equation, uses the square relationship and identifies the energy transfer. To reach the top band, state explicitly that the work done equals $F \times d$ , connect this to $d \propto v^2$ , and say the transfer is by friction.

Top-band response: "The car's kinetic energy is given by $E_k = \dfrac{1}{2}mv^2$ , so it is proportional to the square of the speed. Doubling the speed from $15 \text{ m/s}$ to $30 \text{ m/s}$ therefore makes the kinetic energy $2^2 = 4$ times greater. To stop the car, the braking force must do work equal to this kinetic energy: $F \times d = \dfrac{1}{2}mv^2$ . For the same braking force $F$ , the braking distance $d$ is proportional to $v^2$ , so it too becomes about four times as long. During braking, friction between the brake pads and the discs transfers the car's kinetic energy into the thermal (internal) energy store of the brakes, which is why the brakes get hot."

Examiner-style commentary: Full marks. It quotes and applies $E_k = \dfrac{1}{2}mv^2$ , links the work done ( $F \times d$ ) to the braking distance, states the fourfold increase with justification, and describes the kinetic-to-thermal transfer by friction, naming both the mechanism and the destination store.

Summary

Typical speeds worth a rough sense of scale: walking $\approx 1.5 \text{ m/s}$ , running $\approx 3 \text{ m/s}$ , a town car $\approx 13 \text{ m/s}$ , a motorway car $\approx 31 \text{ m/s}$ .
Stopping distance = thinking distance + braking distance, measured in metres.
Thinking distance depends on speed and reaction time; reaction time is increased by tiredness, alcohol, drugs and distractions.
Braking distance depends on speed, mass and the braking force, which is reduced by wet/icy roads, worn tyres and worn brakes.
During braking, the car's kinetic energy is transferred to the thermal store of the brakes by friction.
Because $E_k = \dfrac{1}{2}mv^2$ , braking distance is proportional to speed squared: double the speed and the braking distance becomes about four times as long.

This content is aligned with OCR Gateway Combined Science A (J250), Topic P6 Global challenges. Refer to the official OCR specification for exact wording.

Speed, Reaction Time and Stopping Distances

Speed, Reaction Time and Stopping Distances

Some Typical Speeds

Stopping Distance = Thinking Distance + Braking Distance

Factors Affecting Thinking Distance

Factors Affecting Braking Distance

Energy Transfer When a Car Brakes

Why Braking Distance Grows with the Square of the Speed

Worked Example 1 — The effect of doubling speed

Worked Example 2 — Using the kinetic energy directly

Typical Stopping Distances

Common Misconceptions

Model Answer — Explaining Braking Distance and Speed

Summary

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