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AQA GCSE Physics · Topic 4.5 Forces · Combined and Triple
Edexcel International GCSE Physics · Section 1 Forces and motion
Stopping Distance
In this lesson you'll learn to: use stopping distance = thinking distance + braking
distance; calculate thinking distance (speed × reaction time) and braking distance
(½mv² ÷ braking force); explain the factors that increase each one; and read both from a
velocity–time graph.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. A fallen tree is 60 m ahead. Press Hazard! Brake and see if the car stops in time. Then make the driver tired, or on a phone; make the road wet or icy; load the car up; go faster. Keep a run, change one thing, and compare the two velocity–time graphs.
Speed — and the driver (thinking distance)
reaction time = 0.70 s
The car and the road (braking distance)
braking force = 9000 N
A fallen tree is 60 m ahead when the driver sees it.
thinking distance
—
speed × reaction time
braking distance
—
½mv² ÷ braking force
stopping distance
—
thinking + braking
Where ½mv² ÷ F comes from. To stop, the brakes do work that removes all the car's kinetic energy: work done = force × distance and kinetic energy = ½mv², so F × d = ½mv² and braking distance = ½mv² ÷ F. Double the speed and the braking distance goes up four times.
Click a factor, then click the list it belongs in. Careful — one goes in both.
Thinking distance depends on the driver (and the speed). Braking distance depends on the car and the road (and the speed).
The flat part is the thinking time: the car is still at full speed while the driver reacts.
The sloping part is the braking. Distance = area under the graph.
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▲ In Read the graph, press What if the driver was tired? — a favourite exam sketch.
The driver controls the thinking distance. The car and the road control the braking distance.
And speed affects both. The notes below give you the equations, the factors, and how to read the two distances off a velocity–time graph.
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Revision notes
⭐ The word equation
stopping distance = thinking distance + braking distance
- Thinking distance — how far the car travels while the driver reacts, between seeing the hazard and pressing the brake. The car is still at full speed.
- Braking distance — how far the car travels once the brakes are on, until it stops.
Thinking distance
thinking distance = speed × reaction time — it's just distance = speed × time, for the time the driver takes to react. A typical reaction time is 0.2 s to 0.9 s.
Thinking distance goes up if the reaction time goes up, or the speed goes up. Things that make reaction time longer:
- tiredness
- alcohol or drugs
- distractions — using a phone, talking, the radio
Braking distance
When the driver brakes, the brakes do work on the car. That work removes all of the car's kinetic energy, which is transferred to thermal energy in the brakes (they get hot):
work done by the brakes = kinetic energy lost → F × d = ½mv² → braking distance d = ½mv² ÷ F, where F is the braking force.
So braking distance goes up if:
- the car is going faster — and because v is squared, doubling the speed makes the braking distance four times as long;
- the car is more massive — a heavy load means more kinetic energy to remove;
- the braking force is smaller — wet or icy roads and worn tyres give less friction (grip) between the tyres and the road; worn brakes give less friction in the brakes.
| Increases THINKING distance | Increases BRAKING distance |
|---|---|
| tiredness | wet road |
| alcohol | icy road |
| drugs | worn tyres |
| using a phone (distraction) | worn brakes |
| speed | speed |
| heavy load (more mass) |
⚠ Trap 1 — alcohol does not affect the brakes
Tiredness, alcohol, drugs and phones affect the driver, so they change the thinking distance only. The road, the tyres, the brakes and the load affect the car, so they change the braking distance only. Speed is the one that changes both.
Stopping on a velocity–time graph
- The flat part is the reaction time — still at full speed. Its area (a rectangle) is the thinking distance.
- The sloping part is braking. Its area (a triangle) is the braking distance, and its gradient is the deceleration.
- Total area = stopping distance.
⚠ Trap 2 — sketching the tired (or drunk) driver
Same speed, so the line starts at the same height. A longer flat part, because the reaction time is longer. Then a braking line parallel to the first one — same car, same road, so the same deceleration and the same braking distance. For an icy road it's the other way round: the same flat part, then a shallower slope.
AQA Higher Estimating braking forces. Use F = ½mv² ÷ d, or find
the deceleration a = v ÷ t and then F = m × a. A typical car (about 1500 kg) braking hard from
30 m/s decelerates at about 6–8 m/s² — a braking force of roughly 10 000 N. Large
decelerations can make the brakes overheat and the car skid.
How to write it in the exam
"Explain how [factor] affects the stopping distance"
[factor] increases the
reaction time / kinetic energy / … reduces the friction, so the
thinking / braking distance increases, so the stopping distance increases.
name the factor say what it changes say which distance, then the total
A car travels at 20 m/s. The driver's reaction time is 0.6 s. Calculate the thinking distance.
thinking distance = speed × reaction time = 20 × 0.6 = 12 m
A 1200 kg car at 15 m/s brakes with a force of 6000 N. Calculate the braking distance.
KE = ½mv² = ½ × 1200 × 15² = 135 000 J. Work done = F × d, so d = 135 000 ÷ 6000 = 22.5 m
The car above now travels at 30 m/s. What happens to its braking distance?
The speed has doubled, and braking distance depends on v², so it goes up four times, to 90 m.
A driver is very tired and it is raining. Explain how these affect the stopping distance. (6 marks)
Being tired increases the reaction time, so the thinking distance increases. Rain makes the road wet, which reduces the friction between the tyres and the road, so the braking force is smaller and the braking distance increases. Stopping distance = thinking + braking, so the stopping distance increases. The driver should slow down and leave a bigger gap.
✅ Check your answer
Named which distance (thinking or braking) each factor changes · said why (reaction time, or friction / kinetic energy) · finished with the stopping distance · units on every calculation.
📘 Now do it in your workbook
Write the word equation, sort the ten factors, read the velocity–time graph, and write the six-mark answer.
Edexcel iGCSE Forces and Motion Workbook · page 9 AQA GCSE Physics Workbook · FORCES · page 16✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this topic.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Everything above, explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the workbook page above cover every mark.
Now put it into practice
Page 9 of the Forces and Motion workbook is free: the word equation, the factor sort, a velocity–time graph question and a six-mark answer.
Page 16 of the Forces workbook has the word equation, the factor sort, a velocity–time graph question and a six-mark answer, with full answers at the back.
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