Forces, stopping and braking

What you'll learn

How human reaction time can be measured, and what typical values look like.
Why stopping distance is split into thinking distance and braking distance.
How speed, mass, brakes, road conditions and tyre grip affect stopping.
How large decelerations can cause dangerous forces, including Higher Tier estimates.

Before we start: slowing down is acceleration too

In physics, velocity means speed in a chosen direction. If a car slows down, its velocity is changing, so it is accelerating — just in the opposite direction to its motion.

Definition

Deceleration

Deceleration is acceleration that reduces the speed of an object. In calculations it may appear as a negative acceleration, but exams often ask for its size, which is positive.

The useful equation is:

a=Δvta=\frac{\Delta v}{t}

where $a$ is acceleration in metres per second squared, $Δv\Delta v$ is change in velocity in metres per second, and $t$ is time in seconds.

A resultant force is the single overall force after all forces on an object are combined. If there is a resultant force backwards on a moving car, the car decelerates.

Reaction time

Definition

Reaction time

Reaction time is the time between noticing a stimulus, such as a hazard, and starting to respond, such as pressing the brake pedal.

A simple way to measure reaction time is the ruler-drop test. One person holds a ruler vertically with the zero mark level with another person’s fingers. The ruler is released without warning. The catcher catches it, and the distance it falls is recorded. A larger distance means a longer reaction time.

A labelled ruler-drop reaction-time test showing distance fallen and catch point

Another method is a computer or phone test: a light, colour or symbol appears at a random time, and you press a key or screen as quickly as possible. The device records the time.

Typical simple reaction times are about 0.2 to 0.3 seconds. Real driving responses can be longer, often around 0.5 to 1.0 seconds, because the driver must notice, understand and decide what to do.

Example

Interpreting a ruler-drop result

A pupil catches a ruler after it has fallen 18 cm. Another pupil catches it after 28 cm.

The smaller distance means the ruler had less time to fall, so the 18 cm result shows the faster reaction.
Using a conversion chart, 18 cm is about 0.19 s and 28 cm is about 0.24 s.
The difference is about 0.05 s, so the first pupil reacted faster by roughly five hundredths of a second.

Tip

Improving reliability

Repeat the test several times and calculate a mean, keep the starting position and hand the same, release the ruler at random times, and ignore obvious anomalies caused by laughing, anticipation or missed catches.

What affects reaction time?

A driver’s reaction time can increase because of:

alcohol or drugs, including some medicines that cause drowsiness
tiredness
distractions, such as a phone, passengers or loud music
poor visibility or a complicated road situation

A longer reaction time means the car travels further before braking even begins.

Example

Extra thinking distance from distraction

A car travels at 18 m/s. A driver’s reaction time increases from 0.7 s to 1.2 s because they are distracted.

Find the extra reaction time: $s1.2\ \text{s}-0.7\ \text{s}=0.5\ \text{s}$ .
Use distance = speed × time for the extra distance: $m18\ \text{m/s}\times 0.5\ \text{s}=9\ \text{m}$ .
The car travels an extra 9 m before the brakes are even applied.

Stopping distance

Definition

Stopping distance

Stopping distance is the total distance travelled from the moment the driver sees a hazard to the moment the vehicle stops.

It has two parts: thinking distance, while the driver reacts, and braking distance, while the brakes slow the vehicle down.

A car stopping-distance diagram showing thinking distance plus braking distance equals stopping distance

Key Idea

The relationship to recall

You should recall that:

sstopping=sthinking+sbrakings_{\text{stopping}}=s_{\text{thinking}}+s_{\text{braking}}

Thinking distance is mainly affected by the car’s speed and the driver’s reaction time. Braking distance is mainly affected by the car’s speed, mass, brakes, road surface and tyre-road friction.

Common Mistake

Mixing up the two distances

Reaction time affects thinking distance, not braking distance. Brake condition, tyre grip and road surface affect braking distance, not thinking distance. Speed affects both.

Braking distance and friction

Definition

Friction

Friction is a contact force that opposes sliding or relative motion between surfaces.

When a car brakes, the brake system slows the wheels, but the force that slows the whole car comes from friction between the tyres and the road. Less grip means a smaller braking force, so the braking distance increases.

Factors that increase braking distance include:

greater mass of the vehicle, because a heavier vehicle has more kinetic energy at the same speed
greater speed, because the moving vehicle has much more energy
worn or faulty brakes, because they provide a smaller braking force
wet, icy, oily or loose road surfaces, because they reduce friction
worn tyres or poor tyre pressure, because the tyres grip the road less well

Definition

Kinetic energy and work done

Kinetic energy is the energy an object has because it is moving. Work done is energy transferred by a force moving an object through a distance in the force’s direction.

The key idea is that braking transfers the car’s kinetic energy to the surroundings, mainly as thermal energy in the brakes, tyres and road.

Why speed is such a big deal

Thinking distance is directly proportional to speed if reaction time stays the same. So doubling speed doubles thinking distance.

Braking distance rises much faster. For the same car and same average braking force, braking distance is proportional to the square of the speed: $d∝v2d\propto v^2$ . So doubling speed makes braking distance about four times bigger.

A graph showing thinking distance increasing linearly with speed, while braking and total stopping distance curve upwards

The speed-estimation and work-done calculation parts are Separate Physics content in Edexcel because the spec points are marked P.

The useful equations are:

Ek=12mv2W=Fd\begin{aligned} E_k &= \frac{1}{2}mv^2 \\ W &= Fd \end{aligned}

For braking, the work done by the braking force equals the initial kinetic energy of the vehicle:

Fd=12mv2Fd=\frac{1}{2}mv^2

Example

Estimating stopping distance using work done

A 1200 kg car travels at 20 m/s. The driver’s reaction time is 0.7 s. The average braking force is 6000 N.

Calculate the thinking distance: $ms=vt=20\ \text{m/s}\times 0.7\ \text{s}=14\ \text{m}$ .
Calculate the initial kinetic energy: $JE_k=\frac{1}{2}\times 1200\ \text{kg}\times \left(20\ \text{m/s}\right)^2=240000\ \text{J}$ .
Use work done by the brakes: $md=\frac{W}{F}=\frac{240000\ \text{J}}{6000\ \text{N}}=40\ \text{m}$ .
Add the two parts: stopping distance = 14 m + 40 m = 54 m.
If the speed increased to 30 m/s, the braking distance would scale by $(3020)2=2.25\left(\frac{30}{20}\right)^2=2.25$ , so the braking distance would become about 90 m before adding the thinking distance.

Common Mistake

Model assumptions

The work-done method assumes a roughly constant average braking force and a level road. Real stopping distances vary with tyres, road surface, brakes, weather and driver response.

Large decelerations and danger

A large deceleration means a big change in velocity in a short time. This is dangerous because the force on the person or vehicle can be very large.

Using Newton’s second law:

F = ma

a larger deceleration produces a larger force for the same mass. This is why seatbelts, airbags and crumple zones help: they increase the time and distance over which the person stops, reducing the deceleration and therefore reducing the force.

The force-estimation part is Higher Tier only in the Edexcel wording.

Example

Estimating force during a sudden stop

A 70 kg passenger in a car travelling at 13 m/s is brought to rest in 0.20 s during a crash.

Find the size of the deceleration: $m/s2a=\frac{13\ \text{m/s}}{0.20\ \text{s}}=65\ \text{m/s}^2$ .
Use $F = ma$ : $NF=70\ \text{kg}\times 65\ \text{m/s}^2=4550\ \text{N}$ .
The force is about 4.6 kN, which is very large. If the stopping time were increased, the force would be smaller.

Exam technique

In the exam

Decide whether the question is about thinking distance, braking distance or total stopping distance before choosing your explanation.
Keep units consistent: speeds in m/s, time in s, distances in m, forces in N and energy in J.
For speed changes, remember the key pattern: thinking distance scales with speed, but braking distance scales with speed squared.

Self review

Check yourself

A driver is tired. Which part of stopping distance increases first, and why?
Why does doubling a vehicle’s speed more than double its total stopping distance?
How do crumple zones reduce the force on passengers during a crash?

Forces, stopping and braking

What you'll learn

How human reaction time can be measured, and what typical values look like.
Why stopping distance is split into thinking distance and braking distance.
How speed, mass, brakes, road conditions and tyre grip affect stopping.
How large decelerations can cause dangerous forces, including Higher Tier estimates.

Before we start: slowing down is acceleration too

In physics, velocity means speed in a chosen direction. If a car slows down, its velocity is changing, so it is accelerating — just in the opposite direction to its motion.

Definition

Deceleration

Deceleration is acceleration that reduces the speed of an object. In calculations it may appear as a negative acceleration, but exams often ask for its size, which is positive.

The useful equation is:

a=Δvta=\frac{\Delta v}{t}

where $a$ is acceleration in metres per second squared, $Δv\Delta v$ is change in velocity in metres per second, and $t$ is time in seconds.

A resultant force is the single overall force after all forces on an object are combined. If there is a resultant force backwards on a moving car, the car decelerates.

Reaction time

Definition

Reaction time

Reaction time is the time between noticing a stimulus, such as a hazard, and starting to respond, such as pressing the brake pedal.

A labelled ruler-drop reaction-time test showing distance fallen and catch point

Another method is a computer or phone test: a light, colour or symbol appears at a random time, and you press a key or screen as quickly as possible. The device records the time.

Typical simple reaction times are about 0.2 to 0.3 seconds. Real driving responses can be longer, often around 0.5 to 1.0 seconds, because the driver must notice, understand and decide what to do.

Example

Interpreting a ruler-drop result

A pupil catches a ruler after it has fallen 18 cm. Another pupil catches it after 28 cm.

The smaller distance means the ruler had less time to fall, so the 18 cm result shows the faster reaction.
Using a conversion chart, 18 cm is about 0.19 s and 28 cm is about 0.24 s.
The difference is about 0.05 s, so the first pupil reacted faster by roughly five hundredths of a second.

Tip

Improving reliability

What affects reaction time?

A driver’s reaction time can increase because of:

alcohol or drugs, including some medicines that cause drowsiness
tiredness
distractions, such as a phone, passengers or loud music
poor visibility or a complicated road situation

A longer reaction time means the car travels further before braking even begins.

Example

Extra thinking distance from distraction

A car travels at 18 m/s. A driver’s reaction time increases from 0.7 s to 1.2 s because they are distracted.

Find the extra reaction time: $s1.2\ \text{s}-0.7\ \text{s}=0.5\ \text{s}$ .
Use distance = speed × time for the extra distance: $m18\ \text{m/s}\times 0.5\ \text{s}=9\ \text{m}$ .
The car travels an extra 9 m before the brakes are even applied.

Stopping distance

Definition

Stopping distance

Stopping distance is the total distance travelled from the moment the driver sees a hazard to the moment the vehicle stops.

It has two parts: thinking distance, while the driver reacts, and braking distance, while the brakes slow the vehicle down.

A car stopping-distance diagram showing thinking distance plus braking distance equals stopping distance

Key Idea

The relationship to recall

You should recall that:

sstopping=sthinking+sbrakings_{\text{stopping}}=s_{\text{thinking}}+s_{\text{braking}}

Common Mistake

Mixing up the two distances

Reaction time affects thinking distance, not braking distance. Brake condition, tyre grip and road surface affect braking distance, not thinking distance. Speed affects both.

Braking distance and friction

Definition

Friction

Friction is a contact force that opposes sliding or relative motion between surfaces.

Factors that increase braking distance include:

greater mass of the vehicle, because a heavier vehicle has more kinetic energy at the same speed
greater speed, because the moving vehicle has much more energy
worn or faulty brakes, because they provide a smaller braking force
wet, icy, oily or loose road surfaces, because they reduce friction
worn tyres or poor tyre pressure, because the tyres grip the road less well

Definition

Kinetic energy and work done

Kinetic energy is the energy an object has because it is moving. Work done is energy transferred by a force moving an object through a distance in the force’s direction.

The key idea is that braking transfers the car’s kinetic energy to the surroundings, mainly as thermal energy in the brakes, tyres and road.

Why speed is such a big deal

Thinking distance is directly proportional to speed if reaction time stays the same. So doubling speed doubles thinking distance.

A graph showing thinking distance increasing linearly with speed, while braking and total stopping distance curve upwards

The speed-estimation and work-done calculation parts are Separate Physics content in Edexcel because the spec points are marked P.

The useful equations are:

Ek=12mv2W=Fd\begin{aligned} E_k &= \frac{1}{2}mv^2 \\ W &= Fd \end{aligned}

For braking, the work done by the braking force equals the initial kinetic energy of the vehicle:

Fd=12mv2Fd=\frac{1}{2}mv^2

Example

Estimating stopping distance using work done

A 1200 kg car travels at 20 m/s. The driver’s reaction time is 0.7 s. The average braking force is 6000 N.

Calculate the thinking distance: $ms=vt=20\ \text{m/s}\times 0.7\ \text{s}=14\ \text{m}$ .
Calculate the initial kinetic energy: $JE_k=\frac{1}{2}\times 1200\ \text{kg}\times \left(20\ \text{m/s}\right)^2=240000\ \text{J}$ .
Use work done by the brakes: $md=\frac{W}{F}=\frac{240000\ \text{J}}{6000\ \text{N}}=40\ \text{m}$ .
Add the two parts: stopping distance = 14 m + 40 m = 54 m.
If the speed increased to 30 m/s, the braking distance would scale by $(3020)2=2.25\left(\frac{30}{20}\right)^2=2.25$ , so the braking distance would become about 90 m before adding the thinking distance.

Common Mistake

Model assumptions

The work-done method assumes a roughly constant average braking force and a level road. Real stopping distances vary with tyres, road surface, brakes, weather and driver response.

Large decelerations and danger

A large deceleration means a big change in velocity in a short time. This is dangerous because the force on the person or vehicle can be very large.

Using Newton’s second law:

F = ma

The force-estimation part is Higher Tier only in the Edexcel wording.

Example

Estimating force during a sudden stop

A 70 kg passenger in a car travelling at 13 m/s is brought to rest in 0.20 s during a crash.

Find the size of the deceleration: $m/s2a=\frac{13\ \text{m/s}}{0.20\ \text{s}}=65\ \text{m/s}^2$ .
Use $F = ma$ : $NF=70\ \text{kg}\times 65\ \text{m/s}^2=4550\ \text{N}$ .
The force is about 4.6 kN, which is very large. If the stopping time were increased, the force would be smaller.

Exam technique

In the exam

Decide whether the question is about thinking distance, braking distance or total stopping distance before choosing your explanation.
Keep units consistent: speeds in m/s, time in s, distances in m, forces in N and energy in J.
For speed changes, remember the key pattern: thinking distance scales with speed, but braking distance scales with speed squared.

Self review

Check yourself

A driver is tired. Which part of stopping distance increases first, and why?
Why does doubling a vehicle’s speed more than double its total stopping distance?
How do crumple zones reduce the force on passengers during a crash?

Forces, stopping and braking

What you'll learn

Before we start: slowing down is acceleration too

Reaction time

What affects reaction time?

Stopping distance

Braking distance and friction

Why speed is such a big deal

Large decelerations and danger

Recap questions

Forces, stopping and braking

What you'll learn

Before we start: slowing down is acceleration too

Reaction time

What affects reaction time?

Stopping distance

Braking distance and friction

Why speed is such a big deal

Large decelerations and danger

Recap questions

Forces, stopping and braking

What you'll learn

Before we start: slowing down is acceleration too

Reaction time

What affects reaction time?

Stopping distance

Braking distance and friction

Why speed is such a big deal

Large decelerations and danger

Recap questions

Forces, stopping and braking Revision Guide

Forces, stopping and braking

What you'll learn

Before we start: slowing down is acceleration too

Reaction time

What affects reaction time?

Stopping distance

Braking distance and friction

Why speed is such a big deal

Large decelerations and danger

Recap questions

Forces, stopping and braking Revision Guide