P18: Stopping Distances
Understanding thinking distance, braking distance, overall stopping distance, factors that affect each component, the relationship between kinetic energy and braking, and road safety.
Stopping Distance
Stopping distance = Thinking distance + Braking distance
Stopping distance is the total distance a vehicle travels from the moment a driver sees a hazard to the moment the vehicle comes to a complete stop. It is the sum of the thinking distance and the braking distance.
| Component | Definition | What happens |
|---|---|---|
| Thinking distance | Distance travelled during the driver's reaction time | Driver perceives hazard and applies brakes; vehicle travels at constant speed |
| Braking distance | Distance travelled while the brakes are applied | Braking force decelerates the vehicle to rest |
| Stopping distance | Total distance from seeing hazard to stopping | Sum of thinking and braking distances |
Thinking Distance
Thinking distance = speed × reaction time
Thinking distance is directly proportional to both the speed of the vehicle and the driver's reaction time. If either doubles, the thinking distance doubles.
Worked Example
A car is travelling at 20 m/s and the driver has a reaction time of 0.6 s. Calculate the thinking distance.
Thinking distance = 20 × 0.6 = 12 m
Factors that increase thinking distance:
- Higher speed - the car travels further during the same reaction time
- Tiredness - increases reaction time
- Alcohol and drugs - increase reaction time and impair judgement
- Distractions - using a phone, talking to passengers, adjusting controls
- Medication - some medicines cause drowsiness and slow reactions
Speed affects both thinking distance and braking distance. Thinking distance is proportional to speed, but braking distance is proportional to speed². This means braking distance increases much more rapidly with speed.
Braking Distance
Braking distance is the distance a vehicle travels under the braking force. It depends on the speed of the vehicle and the braking force available, as well as road and vehicle conditions.
Factors that increase braking distance:
- Higher speed - more kinetic energy to transfer, and speed² relationship
- Wet or icy roads - reduce friction between tyres and road
- Worn tyres - reduced tread depth means less grip
- Worn brake pads - reduced braking force
- Heavy loads - more mass means more kinetic energy to dissipate
- Downhill gradient - component of weight adds to the forward motion
| Speed (mph) | Thinking distance (m) | Braking distance (m) | Stopping distance (m) |
|---|---|---|---|
| 20 | 6 | 6 | 12 |
| 30 | 9 | 14 | 23 |
| 40 | 12 | 24 | 36 |
| 50 | 15 | 38 | 53 |
| 60 | 18 | 55 | 73 |
| 70 | 21 | 75 | 96 |
Braking distance increases with the square of the speed. Doubling the speed roughly quadruples the braking distance. This is because kinetic energy is proportional to speed².
Kinetic Energy and Braking (Higher)
Kinetic energy = ½mv²
Eₖ = ½mv²
Eₖ = kinetic energy (J), m = mass (kg), v = speed (m/s)
When a vehicle brakes, the brakes do work to transfer kinetic energy to thermal energy. The work done by the brakes equals the kinetic energy lost. This is why braking distance is proportional to speed².
Work done by brakes = kinetic energy lost
F × d = ½mv²
F = braking force (N), d = braking distance (m)
Worked Example
A car of mass 1000 kg is travelling at 20 m/s. The braking force is 8000 N. Calculate the braking distance.
Work done = ½mv² = 0.5 × 1000 × 20² = 200 000 J
F × d = 200 000
d = 200 000 / 8000 = 25 m
Worked Example - Effect of Speed
The same car now travels at 40 m/s (double the speed) with the same braking force of 8000 N. Calculate the new braking distance.
Work done = 0.5 × 1000 × 40² = 800 000 J
d = 800 000 / 8000 = 100 m
Notice: doubling the speed quadruples the braking distance (from 25 m to 100 m).
From F × d = ½mv², we get d = ½mv² / F. This shows that braking distance is directly proportional to the square of the speed and inversely proportional to the braking force.
Braking Force and Deceleration
The braking force causes the vehicle to decelerate. Using F = ma, a larger braking force produces a larger deceleration. The braking distance decreases with larger braking force.
Braking distance = ½mv² / F
Or from the equations of motion: v² = u² + 2as → s = u² / (2a) where a = F/m
Worked Example
A car of mass 1200 kg travelling at 25 m/s has a braking force of 6000 N. Calculate the deceleration and braking distance.
Deceleration a = F/m = 6000/1200 = 5 m/s²
Braking distance s = u²/(2a) = 25²/(2 × 5) = 625/10 = 62.5 m
Large decelerations mean a large braking force is needed. This can cause the brakes to overheat and the vehicle to skid, losing control. In extreme cases, very large decelerations can injure occupants.
Road Safety
Understanding stopping distances is crucial for road safety. Speed limits are set to ensure that drivers can stop safely within the distance they can see ahead.
Key road safety measures:
- Speed limits - reduce stopping distances by limiting speed
- Seat belts - increase stopping time for occupants, reducing force
- Airbags - cushion impact and increase stopping time
- Crumple zones - absorb energy and increase stopping distance of the car body
- ABS (Anti-lock Braking System) - prevents wheels locking so the driver can steer while braking
Leaving a larger gap between vehicles is important because at higher speeds the stopping distance is much greater. The typical advice is to leave at least a two-second gap in good conditions, and double this in wet weather.
When explaining how speed affects stopping distance, make sure to distinguish between thinking distance (proportional to speed) and braking distance (proportional to speed²). This is a very common exam question.
Measuring Reaction Time
Reaction time can be measured using a simple ruler drop test:
- One person holds a ruler vertically with the 0 cm mark between the other person's thumb and forefinger.
- The ruler is dropped without warning and the person catches it as quickly as possible.
- The distance the ruler falls is recorded.
- Use the equation s = ½gt² to calculate the reaction time: t = √(2s/g)
Worked Example
In a ruler drop test, the ruler falls 18 cm (0.18 m) before being caught. Calculate the reaction time.
s = ½gt² → 0.18 = 0.5 × 9.8 × t²
t² = 0.18 / 4.9 = 0.0367
t = √0.0367 = 0.19 s
Typical human reaction times are 0.2 to 0.4 seconds. Tiredness, alcohol, and distractions all increase reaction time, which increases thinking distance and therefore stopping distance.
Weather Conditions
Different weather conditions significantly affect stopping distances:
| Condition | Effect on thinking distance | Effect on braking distance |
|---|---|---|
| Dry road | Normal | Normal |
| Wet road | No change | Up to double |
| Icy road | No change | Up to ten times |
| Fog | No change (but driver may react late) | No change |
Weather conditions mainly affect braking distance through reduced friction. Wet roads reduce tyre grip, meaning the braking force is less and the vehicle takes longer to stop. Icy roads are even more dangerous as friction is greatly reduced.
Practice Questions
1. A driver travelling at 30 m/s has a reaction time of 0.5 s. Calculate the thinking distance.
Thinking distance = 30 × 0.5 = 15 m.
2. A car of mass 800 kg is travelling at 15 m/s. The braking force is 5000 N. Calculate the braking distance.
Kinetic energy = 0.5 × 800 × 15² = 90 000 J. Braking distance = 90 000 / 5000 = 18 m.
3. Explain why doubling the speed of a car more than doubles the stopping distance.
Thinking distance doubles (proportional to speed). Braking distance quadruples (proportional to speed² because kinetic energy = ½mv²). Since stopping distance = thinking + braking, the total more than doubles because braking distance increases at a greater rate.
4. State three factors that affect thinking distance and three that affect braking distance.
Thinking distance: speed, reaction time (affected by tiredness, alcohol, drugs, distractions, medication). Braking distance: speed, road conditions (wet, icy), tyre condition, brake condition, vehicle mass, gradient.
5. A car travelling at 20 m/s has a total stopping distance of 38 m. The thinking distance is 10 m. Calculate the braking distance and the braking force if the car's mass is 1000 kg.
Braking distance = 38 - 10 = 28 m. KE = 0.5 × 1000 × 20² = 200 000 J. Braking force = 200 000 / 28 = 7143 N.
Maths Skills
Stopping Distance = Thinking Distance + Braking Distance
Thinking distance = speed × reaction time (directly proportional to speed). Braking distance can be calculated from v² = u² + 2as, rearranged as s = u²/(2a) where a = Fbrake/m. This shows braking distance is proportional to speed squared.
Worked Example
A car travels at 30 m/s. The driver's reaction time is 0.7 s. The braking deceleration is 8 m/s². Calculate the total stopping distance.
Thinking distance = 30 × 0.7 = 21 m
Braking distance = u²/(2a) = 30²/(2 × 8) = 900/16 = 56.25 m
Total stopping distance = 21 + 56.25 = 77.25 m
Proportional Relationships
Thinking distance ∝ speed (if reaction time is constant). Braking distance ∝ speed² (because kinetic energy = ½mv²). This means doubling the speed doubles the thinking distance but quadruples the braking distance. The overall stopping distance more than doubles when speed doubles.
Worked Example
At 20 m/s, a car has thinking distance 14 m and braking distance 25 m. Estimate the stopping distance at 40 m/s (same car, same road).
Thinking distance doubles: 14 × 2 = 28 m
Braking distance quadruples: 25 × 4 = 100 m
Total = 28 + 100 = 128 m (compared to 39 m at 20 m/s)
Common Misconceptions
Doubling Speed and Stopping Distance
Doubling the speed doubles the stopping distance. Doubling the speed doubles the thinking distance but roughly quadruples the braking distance (because KE ∝ v²). Since braking distance is usually the larger component at higher speeds, the total stopping distance more than doubles. For example, at 70 mph the stopping distance is about 96 m, while at 35 mph it is only about 21 m — more than four times greater, not twice.
Factors Affecting Stopping Distance
Only speed affects stopping distance. Many factors affect both components: thinking distance is affected by reaction time (tiredness, alcohol, drugs, distractions, age) and speed. Braking distance is affected by speed, road conditions (wet, icy), tyre condition, brake condition, vehicle mass, and gradient. A driver on icy tyres at the speed limit can have a far greater stopping distance than a sober driver with new tyres slightly below the limit.
6-Mark Extended Question
Explain why speed limits are important for road safety, discussing both thinking distance and braking distance. [6 marks]
Speed limits are set to ensure that drivers can stop safely within the distance they can see ahead (1). As speed increases, thinking distance increases proportionally because the car travels further during the driver's reaction time (1). More importantly, braking distance increases with the square of speed because kinetic energy is proportional to v² (1). This means that a small increase in speed at high speeds causes a much larger increase in stopping distance than the same increase at low speeds (1). Speed limits therefore limit the maximum stopping distance to a manageable level for the road conditions (1). Without speed limits, drivers would routinely travel at speeds where they could not stop in time for unexpected hazards, leading to more frequent and more severe collisions. In wet or icy conditions, even lower speeds are needed because braking distance increases further (1).
AO3: Analyse and Evaluate
The table shows typical stopping distances at different speeds for a car on a dry road:
| Speed (mph) | Speed (m/s) | Thinking distance (m) | Braking distance (m) | Total stopping distance (m) |
|---|---|---|---|---|
| 20 | 9 | 6 | 6 | 12 |
| 30 | 13 | 9 | 14 | 23 |
| 40 | 18 | 12 | 24 | 36 |
| 50 | 22 | 15 | 38 | 53 |
| 60 | 27 | 18 | 55 | 73 |
| 70 | 31 | 21 | 75 | 96 |
(a) Plot the ratio of braking distance to thinking distance at each speed. What trend do you notice? (b) On a wet road, braking distances are approximately double. Calculate the new total stopping distance at 60 mph. (c) A driver with a 0.2 s slower reaction time (due to tiredness) is travelling at 70 mph. Calculate the additional stopping distance compared to an alert driver.
Evaluation
(a) At 20 mph the ratio is 6/6 = 1.0. At 30 mph it is 14/9 = 1.56. At 40 mph: 24/12 = 2.0. At 50 mph: 38/15 = 2.53. At 60 mph: 55/18 = 3.06. At 70 mph: 75/21 = 3.57. The ratio increases with speed, confirming that braking distance grows much faster than thinking distance.
(b) Wet braking at 60 mph = 55 × 2 = 110 m. Total = 18 + 110 = 128 m (compared to 73 m on a dry road).
(c) Additional thinking distance = extra reaction time × speed = 0.2 × 31 = 6.2 m. The total stopping distance becomes 96 + 6.2 = 102.2 m. Even a small increase in reaction time significantly increases stopping distance at high speed.
📝 Exam Questions by Topic
🎬 Video Resources
Ready to ace your GCSE Physics exams?
Get the best revision books and guides to boost your grades.