Forces and braking

Stopping distance = thinking + braking. The v² trap. Why "friction" alone scores zero. And the alcohol mechanism only 15% of students nail.

SPEC 4.5.6.3 • FORCES — STOPPING DISTANCE & BRAKING

Three Examiner Disasters

This topic appears every paper. Three recent extended-response questions reveal exactly where marks bleed out — and they're the same patterns every year.

15%

Got all 3 marks on the alcohol mechanism (Jun 2024)

17%

Linked distraction to stopping distance correctly (Jun 2023)

4%

Explained where the kinetic energy goes in braking (Jun 2023)

The Pattern

In every case the students knew the right idea but stopped one link short of the full chain. This lesson is about building the complete chain every time — from cause, through mechanism, to consequence — in the language the mark scheme actually rewards.

Stopping Distance = Thinking + Braking

Stopping distance is split into two phases. The driver must see the hazard, react, then brake. Each phase covers distance.

Three Definitions

Thinking distance: the distance the car travels during the driver's reaction time, before the brakes are applied.

Braking distance: the distance the car travels under the braking force, while decelerating to a stop.

Stopping distance = thinking distance + braking distance.

Reaction Time: 0.2–0.9 s

Reaction time is the gap between seeing the hazard and starting to press the brake. The car covers thinking distance during this gap.

Reaction Time (Recall)

For a healthy adult, typical reaction times range from 0.2 s to 0.9 s. AQA expects you to recall this range word-for-word.

thinking distance = speed × reaction time

Why this matters for thinking distance

If reaction time stays the same, doubling the speed doubles the thinking distance. The relationship is linear in speed — thinking distance is proportional to v.

Measuring Reaction Time

The classroom method is the ruler-drop test: a ruler is dropped between the partner's open fingers; the distance fallen gives the reaction time (via equations of motion). Methods using a computer or smartphone reaction test are also acceptable. AQA expects you to be able to describe and evaluate such a method.

What Increases Thinking Distance

Thinking distance is governed by d = v × t_reaction. So two things can make it longer: a slower reaction time, or a higher speed. The spec lists the reaction-time factors explicitly.

Factors that increase reaction time (from spec 4.5.6.3.2)

Tiredness — reduces alertness

Alcohol — impairs the central nervous system

Drugs — illegal drugs and some prescription/legal drugs

Distractions — phone, conversation, eating, other passengers

Speed contribution

Even if the reaction time is unchanged, higher speed means the car covers more distance during the reaction time. Thinking distance scales linearly with speed.

The Mark Lives in the Chain

Mark schemes reward the complete chain — not just naming a factor. Example for alcohol:

alcohol → increased reaction time → increased thinking distance → increased stopping distance.

Stopping at "alcohol slows the driver" is a 1-mark answer at best. The full chain is the difference between 1 mark and 3.

What Increases Braking Distance

Braking distance is set by how much kinetic energy the brakes have to dissipate and how much friction is available to do it. Anything reducing friction, or anything increasing KE, increases braking distance.

FactorMechanism — the bit examiners want

Higher speedGreater KE (∝ v²) must be dissipated by the brakes — more work required, longer braking distance.

Worn brakesReduced friction between brake pads and discs — smaller braking force, smaller deceleration, longer distance.

Worn / under-inflated tyresReduced friction (grip) between tyres and road — same effect: smaller braking force.

Wet, icy, or oily roadReduced friction at the tyre-road contact — wheels can slip; braking force falls.

Greater mass (passengers, load)Greater KE at the same speed (½mv²) — more work required to dissipate it.

Downhill slopeA component of weight acts along the road, opposing the braking force — net decelerating force is reduced.

Spec note

AQA limits "poor condition of the vehicle" to brakes or tyres. Don't invent factors like "engine condition" — they're outside the spec.

The v² Trap

The most-examined idea on this topic — and the one students reliably miss. Thinking distance and braking distance scale with speed differently.

Thinking distance

Linear in v.

d_think = v × t_reaction

Double the speed → double the thinking distance.

Braking distance

Quadratic in v.

KE = ½ m v² and W = F × d

Double the speed → quadruple the braking distance.

Why ∝ v²

The brakes must do enough work to dissipate the car's kinetic energy. Setting work done = kinetic energy:

F × d = ½ m v² ⇒ d = mv² / (2F)

For a fixed braking force F and mass m, the braking distance d is proportional to v². Quadrupling at double speed isn't an opinion — it's algebra.

Worked Example — Scaling

At low speed, thinking distance dominates. As speed rises, braking distance balloons.

SpeedThinking dist. (0.7 s reaction)Braking dist. (assume ∝ v²)Total

10 m/s7 m6 m13 m

20 m/s (×2)14 m (×2)24 m (×4)38 m

30 m/s (×3)21 m (×3)54 m (×9)75 m

The Common Wrong Answer

Many students write "braking distance is proportional to speed" or "both distances double when speed doubles". Both are wrong.

From 10 to 20 m/s the braking distance jumps from 6 m to 24 m — a factor of 4, not 2. From 10 to 30 m/s it goes from 6 m to 54 m — a factor of 9.

In One Sentence

"Doubling speed quadruples the kinetic energy that the brakes must dissipate, so the braking distance quadruples." Memorise that line.

Reading a Stopping-Distance Graph

AQA frequently asks you to read a thinking + braking distance graph and calculate total stopping distance at a given speed. The skill is recognising which line is which.

How to read it

The straight line is thinking distance. Linear → constant gradient = reaction time.

The curved line is braking distance. Curves upward because of v². At higher speeds the gap between the two lines widens dramatically.

Stopping distance = add the two values at your chosen speed.

Where Does the Kinetic Energy Go?

When the brakes are applied, the car loses kinetic energy. That energy doesn't disappear — it's transferred. Naming the mechanism and the destination is what the mark scheme wants.

KE of car ⟶ work done by friction in brakes ⟶ thermal store of brakes (& surroundings)

The Full Chain

The brake pads press onto the brake discs — a contact force.

The friction force between pads and discs does work against the car's motion.

This work transfers energy from the kinetic store of the car to the thermal store of the brakes.

The brakes heat up. (Some energy is also transferred to the surroundings as the brakes radiate / heat the air.)

Useful equation

W = F × d = ½ m v²

Set work done by the braking force equal to the kinetic energy of the car — this is the equation behind every "calculate the braking distance" question, and behind every "explain why it's longer at higher speed" answer.

Worked Calculation — Braking Distance

The energy method is the cleanest route to a braking-distance answer. Set the work done by the brakes equal to the kinetic energy the car loses.

A car of mass 1200 kg travels at 25 m/s. The driver applies the brakes, generating a constant braking force of 7500 N. Calculate the braking distance. 4 MARKS

E

Equation: The work done by the brakes equals the kinetic energy lost. F × d = ½ m v²

S

Substitute: 7500 × d = ½ × 1200 × 25² = ½ × 1200 × 625 = 375 000 J

U

Rearrange: d = 375 000 ÷ 7500

A

Answer: d = 50 m

⚠️

Mark loss check: Forgetting to square the speed turns the KE into 1200 × 25 = 30 000 — six orders of magnitude wrong. Always include the squared in ½mv². Both KE and W = Fs are on the recall list / equation sheet — but you must apply them in the right order.

Alternative route — kinematics

The same answer comes from F = ma to find deceleration, then v² = u² + 2as from the equation sheet. Either route earns full marks; the energy method is usually quicker.

The 4% Trap

On Jun 2023 Paper 2, students were asked why a car's brakes get hot during braking. Only 4% scored both marks. The mistake was almost universal — and avoidable.

✗ 0 marks

"Friction in the brakes makes the brakes get hot."Mark scheme explicitly rejects "friction alone". Missing both required ideas: that work is done, and that the internal/thermal energy of the brakes increases.

✓ 2 marks

"Work is done by the friction force in the brakes; this increases the thermal (internal) energy of the brakes."Two distinct mark scheme points: (1) work is done by friction; (2) the thermal/internal energy of the brakes increases.

Three rejected phrases

Direct from examiner reports — these will not be credited:

"friction" on its own (no mechanism)

"release of energy" (vague — released from what to what?)

"the brakes lose energy" (wrong direction — they gain thermal energy)

Dangers of Large Decelerations

When the braking force is very large — for example, an emergency stop at high speed — the deceleration is large. AQA expects you to explain the dangers.

Two dangers (and they're worth 2 marks)

Brakes overheat. Large deceleration means large braking force, and so a large rate of work done by friction. The brakes' thermal energy rises rapidly, possibly causing brake fade — they become less effective.

Wheels lock; the car skids. If the braking force exceeds the maximum friction at the road, the wheels stop rotating but the car keeps moving. The driver loses steering control and the car can skid out.

F = m × a ⇒ large F ⇒ large a (deceleration)

HT estimate

Higher Tier students should be able to estimate the forces involved in deceleration of a typical road vehicle. Use F = ma with realistic values: car mass ~1000–1500 kg, motorway emergency stop deceleration ~6–8 m/s². That gives braking forces of order 10⁴ N — into the tens of thousands of newtons.

PEE Worked Example — The Alcohol Chain

The "alcohol and stopping distance" question recurs every series — and is the single biggest mark loss in this topic. In Jun 2024, only 15% of students earned all 3 marks. The fix is one complete chain.

Practice question: A driver who has consumed alcohol is approaching a hazard at the speed limit. Explain why the stopping distance of their vehicle will be greater than that of a sober driver. 3 MARKS

P

Point: Alcohol increases the driver's reaction time.

E

Evidence: A longer reaction time means the car travels further between the driver seeing the hazard and pressing the brake — so the thinking distance increases.

E

Explain: Because stopping distance = thinking distance + braking distance, and thinking distance has increased, the total stopping distance increases. Braking distance is unaffected — alcohol does not change the friction in the brakes.

⚠️

Mark loss check: The 85% who lost marks stopped after "alcohol slows the driver" or wrote "alcohol affects the brakes" (wrong mechanism). The chain must reach stopping distance, not stop at reaction time.

Weak vs Strong — Alcohol

Side by side, comparing the answers that examiners reward.

✗ 0 marks

"Alcohol makes the brakes less effective."Wrong mechanism — alcohol affects the driver, not the brakes. None of the three mark scheme points are met.

✓ 3 marks

"Alcohol increases reaction time, increasing thinking distance, which increases total stopping distance."All three mark scheme points named correctly and linked.

✗ 1 mark

"Reaction time gets slower."Imprecise verb (a duration increases, it doesn't "slow"), and the chain stops at reaction time — no link to thinking distance or stopping distance.

✓ 3 marks

"Reaction time increases, so thinking distance increases, so stopping distance increases."Correct verb. Chain reaches stopping distance — all three marks earned.

Pattern to copy

The same three-link chain works for tiredness, drugs, and distractions. Swap the first link, keep the rest. Tiredness → reaction time increases → thinking distance increases → stopping distance increases.

Five Errors That Cost Marks

Patterns examiner reports flag year after year. Fix these now.

Students often writeCorrect version

"Braking distance doubles when speed doubles"Braking distance quadruples when speed doubles — because KE ∝ v²

"Friction makes the brakes hot"Work is done by the friction force, increasing the thermal energy of the brakes

"Alcohol makes the brakes less effective"Alcohol affects the driver : it increases reaction time → thinking distance → stopping distance

"Reaction time gets slower"Reaction time increases (use the correct verb — a duration grows, it doesn't slow)

"Worn tyres" (with no mechanism)Worn tyres → less grip / less friction with the road → smaller braking force → longer braking distance

Examiner Alert

Jun 2023 P2 Q03.5 — "where does the KE go?"

Only 4% of students scored both marks. Mark scheme requires both: (1) work is done due to friction in the brakes, AND (2) the internal/thermal energy of the brakes increases. "Friction" or "the brakes get hot" on its own scored zero.

Jun 2024 P2 Q7.5 — alcohol mechanism

Only 15% of students scored all 3 marks. The losing answers either named the wrong mechanism (alcohol affecting brakes) or stopped one link short (reaction time only, not all the way to stopping distance).

Jun 2023 P2 Q03.4 — distractions on stopping distance

Only 17% got all 3 marks. The chain examiners wanted: distraction → reaction time increases → thinking distance increases → (since stopping = thinking + braking) stopping distance increases. Each link earns a separate mark.

Pattern across all three

Every losing answer was partially right. The marks went to students who wrote the full chain: cause → mechanism → consequence → final quantity. If you only state two of the four, you can't score three marks.

Practice Question

A car travels at 14 m/s on a wet road. The driver, who is feeling tired, sees a hazard ahead.

Explain two different reasons why the car's stopping distance will be greater than the value listed in the Highway Code for a car travelling at 14 m/s.4 MARKS

P1

Reason 1 — Point: The driver is tired.

E1

Evidence + Explain: Tiredness increases the driver's reaction time, so thinking distance increases, increasing total stopping distance.

P2

Reason 2 — Point: The road is wet.

E2

Evidence + Explain: A wet road reduces the friction between the tyres and the road, so the braking force is smaller, the deceleration is smaller, and the braking distance increases — increasing total stopping distance.

⚠️

Mark loss check: Make sure each reason is a different mechanism — one affects thinking distance, one affects braking distance. Writing "tired and distracted" gives two factors but only one mechanism — and the mark scheme will only credit one.

Checkpoint — What You Can Now Do

✅ You can now

Define stopping, thinking, and braking distance — and state the equation stopping = thinking + braking

Recall the typical reaction time range: 0.2–0.9 s for a healthy adult

List and explain the factors affecting thinking distance (tiredness, alcohol, drugs, distractions) and braking distance (speed, brakes, tyres, road conditions, mass, slope)

Explain the v² relationship: thinking ∝ v but braking ∝ v² (because KE = ½mv²)

Calculate a braking distance using F × d = ½ m v² (or via F = ma + v² = u² + 2as)

Describe the energy chain: KE → work done by friction → thermal store of brakes

Explain the dangers of large decelerations: brake overheating, brake fade, loss of control, skidding

Write the alcohol/tiredness/distraction chain in full — three links to stopping distance

Next lesson

5.12 — Momentum (HT only). The vector quantity p = mv, conservation of momentum in collisions and explosions, and (physics only) F = mΔv/Δt.