Forces and motion · GCSE Physics
Stopping distance
Teacher-written GCSE Physics revision on stopping distance: thinking plus braking, reaction-time factors, how braking distance grows with speed squared, and work done by the brakes.
Stopping distance = thinking distance + braking distance. Thinking is speed × reaction time. Braking stores the kinetic energy story: double speed, about four times the braking distance.
The important bits
What you need to know
- 1
Thinking distance is how far the vehicle travels during the driver’s reaction time, before the brakes are applied. At roughly constant speed, thinking distance = speed × reaction time.
- 2
Braking distance is how far the vehicle travels while the brakes are on, until it stops.
- 3
Stopping distance = thinking distance + braking distance. Quote both parts in an explain answer.
- 4
Thinking distance rises with speed and with longer reaction time: alcohol, drugs, distraction, tiredness. It is not about the tyres.
- 5
Braking distance rises with speed, poor brakes, worn tyres, and a wet, icy or gravel road (less friction). A larger mass also needs a larger braking force or a longer distance.
- 6
Kinetic energy ½mv² must be transferred by the work the brakes do, W = Fs. If speed doubles, kinetic energy quadruples, so braking distance roughly quadruples for the same braking force.
- 7
Typical Highway Code values (sense-check, not a substitute for the calculation): at 30 mph thinking 9 m, braking 14 m, stopping 23 m; at 70 mph thinking 21 m, braking 75 m, stopping 96 m.
- 8
Wet roads cut friction, so the same energy is transferred over a longer s in W = Fs. ABS and good tyres are about maintaining a large, controlled F.
Quotations worth analysing
Short evidence. Real method.
“Stopping distance = thinking distance + braking distance”
Split the answer. Alcohol belongs in thinking; ice belongs in braking. Mixing the factors is a standard lost mark.
“Braking distance increases with the square of the speed.”
Because ½mv² must be removed by Fs. Double v, four times the energy, four times s if F stays the same.
Go deeper
Stopping distance is two different physics stories
Thinking distance is how far the car travels during reaction time. At roughly constant speed, it is speed × time, so it doubles if speed doubles (for a fixed reaction time). Alcohol and phones stretch the time, not the brakes. Braking distance is about work done: the brakes must transfer the kinetic store, ½mv², so if speed doubles, kinetic energy quadruples, and braking distance roughly quadruples on the same dry road. That is why speed is so expensive in metres. Wet roads cut friction, so the same energy is transferred over a longer distance. In an answer, split thinking and braking, name a factor for each, and if you have numbers, use v². A six-mark “evaluate speed limits” wants that energy argument, not a slogan about dangerous driving.
Go deeper
Reaction time is a measurement, then a multiplication
School practicals estimate reaction time with a falling ruler: s = ½gt², so t = √(2s/g). A 0.20 m catch with g = 10 m/s² gives t = √(0.040) = 0.20 s, which is optimistic compared with driving. Use the paper’s reaction time. At 20 m/s (72 km/h), 0.70 s of thinking is 14 m before braking even starts. Then add braking distance from energy or from v² = 2as with a negative. Students add 0.70 s to 20 m/s as if the units combined. They do not. Distance = speed × time only when the units are m/s and seconds. Write 20 m/s × 0.70 s = 14 m on one line so the seconds cancel in front of the examiner.
See the idea in action
A 1200 kg car travels at 20 m/s. The driver has a reaction time of 0.50 s. Thinking distance = 20 × 0.50 = 10 m. Kinetic energy = ½mv² = 0.5 × 1200 × 400 = 240 000 J. If the braking force is 8000 N, braking distance from W = Fs is s = 240 000 / 8000 = 30 m. Stopping distance = 10 + 30 = 40 m. At 40 m/s, thinking distance would be 20 m and kinetic energy four times larger, so braking distance about 120 m if the force stayed 8000 N — stopping distance 140 m, a much bigger jump than “twice as fast, twice as far”.
Exam technique
Turn knowledge into marks
Split thinking and braking. Match each factor to the correct part. Use thinking distance = ut and braking from ½mv² = Fs or v² = 2as. Convert mph or km/h to m/s before multiplying.
Common mistakes
Do not give these marks away
- 01
Claiming alcohol increases braking distance — it increases thinking distance (reaction time).
- 02
Saying stopping distance doubles when speed doubles, ignoring the v² dependence of braking distance.
- 03
Adding reaction time to speed without multiplying, or leaving speed in mph inside a metre calculation.
Which factor increases thinking distance but not braking distance?
AIcy road
BWorn brake pads
CThe driver using a mobile phone
DUnderinflated tyres
Show the answer
The driver using a mobile phone. Distraction lengthens reaction time, so thinking distance rises. Ice, worn brakes and poor tyres reduce friction and increase braking distance.
Quick questions
If this is the bit you searched
What factors affect stopping distance?
Thinking distance: speed and reaction time (alcohol, drugs, distraction, tiredness). Braking distance: speed, mass, condition of brakes and tyres, and road surface.
Why does braking distance rise so quickly with speed?
Kinetic energy depends on v². The brakes must do more work, and for a limited friction force that needs a longer distance.
Does a heavier car have a longer thinking distance?
Not from mass itself. Thinking distance is speed × reaction time. A heavier car does have more kinetic energy, so braking distance tends to be longer for the same braking force.
How is reaction time estimated with a ruler?
The ruler falls from rest: s = ½gt². Measure s, rearrange to find t. It is a model of thinking time, not a full driving test.