Stopping distance — AQA GCSE Physics
Test yourself on Stopping distance with AQA GCSE practice questions.
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Stopping distance explained
Stopping a vehicle happens in two stages.
Read the full explanation
During the driver's reaction time the brakes are not yet on, so the vehicle carries on at its original steady speed; the distance covered then is the thinking distance, equal to speed × reaction time. Once the brakes bite, friction does work against the motion and the vehicle decelerates; the distance covered during that is the braking distance, defined as the distance travelled under the braking force. Add the two and you have the stopping distance. On a stacked bar chart or a table of typical values, read both parts separately before adding: at 100 km/h a thinking distance of 20 m and a braking distance of 60 m give a stopping distance of 80 m.
For a given braking force the greater the speed of the vehicle, the greater the stopping distance.
The two parts of the stopping distance grow differently with speed. Thinking distance is speed × reaction time, so it is directly proportional to speed: at a reaction time of 0.6 s, doubling the speed from 10 m/s to 20 m/s doubles the thinking distance from 6 m to 12 m. Braking distance comes from energy. The kinetic energy to be removed is ½ m v², and the work done by the brakes is braking force × braking distance, so with a fixed braking force the braking distance goes with the square of the speed. Doubling the speed from 10 m/s to 20 m/s takes the braking distance from 6 m to 24 m, four times as far. The stopping distance therefore rises far more steeply than the speed.
(Physics only) Students should be able to estimate how the distance for a vehicle to make an emergency stop varies over a range of speeds typical for that vehicle.
An emergency stop can be estimated rather than measured. Take a reaction time of about 0.5 s to 0.7 s and work out thinking distance = speed × reaction time. Then scale the braking distance with the square of the speed from a known value: if a car needs 6 m to brake from 10 m/s, it needs about 24 m from 20 m/s and about 54 m from 30 m/s. Adding the two gives roughly 12 m at 10 m/s, 36 m at 20 m/s and 72 m at 30 m/s, so tripling the speed makes the stop about six times longer. Quote estimates to one or two significant figures in metres, and state the reaction time you assumed. These figures assume the hardest braking a dry road allows; on a wet or icy surface the friction is smaller, so every braking estimate must be increased.
(Physics only) Students will be required to interpret graphs relating speed to stopping distance for a range of vehicles.
Graphs of stopping distance against speed are curved because the braking part grows with the square of the speed while the thinking part grows in proportion to it. Reading one is a matter of care: check the axis quantity and unit, read up from the speed to the curve and across, and compare different vehicles only at the same speed. A loaded lorry sits above a car on such a graph because its greater mass means more kinetic energy, ½ m v², at the same speed, so a given braking force needs a longer distance to remove it. A line for a wet road sits above the dry line for the same vehicle because the friction available at the tyres is smaller. Where two curves are drawn, describe the gap between them as well as each curve, because the difference usually widens as the speed rises.
Your focus
- Calculate a stopping distance by reading thinking and braking distances from a graph and adding them.
- Define braking distance as the distance travelled under the braking force, and thinking distance as speed × reaction time.
- Explain why a distracted driver has a longer stopping distance even though the brakes are unchanged.
Show all 12 objectives
- Show with figures from a table that thinking distance is proportional to speed but braking distance is not.
- Explain, using ½ m v² and work done, why braking distance quadruples when the speed doubles.
- Evaluate a student's claim that both thinking and braking distance are proportional to speed.
- Estimate the stopping distance of a car at 13 m/s and at 31 m/s, stating the reaction time assumed.
- Scale a known braking distance to a new speed using the square of the speed ratio.
- Judge whether a quoted emergency stopping distance is realistic for a car at a given speed.
- Read a stopping distance for a stated speed from a curved graph and give it with the correct unit.
- Compare the stopping distances of a car and a lorry at the same speed and explain the difference using kinetic energy.
- Describe the shape of a stopping distance against speed graph and say what it shows about the two component distances.
Stopping distance exam tips
Marking Points
- one mark for reading the thinking distance and the braking distance separately from the graph or table
- one mark for adding the two distances to give the stopping distance
- one mark for the answer with the unit m
- one mark for defining braking distance as the distance travelled under the braking force
- one mark for stating that the vehicle travels at a steady speed during the driver's reaction time
- one mark for stating that thinking distance is directly proportional to speed
- one mark for supporting that with figures, such as 6 m at 10 m/s rising to 12 m at 20 m/s
- one mark for stating that braking distance is not proportional to speed but increases more steeply
- one mark for the supporting braking figures, such as 6 m at 10 m/s rising to 24 m at 20 m/s
- one mark for a stated reaction time in the typical range 0.2 s to 0.9 s
- one mark for calculating the thinking distance as speed × reaction time
- one mark for scaling the braking distance with the square of the speed
- one mark for adding the two parts to give an estimated stopping distance in metres
- one mark for the braking distance scaled correctly, such as about 24 m at 20 m/s scaled from 6 m at 10 m/s
- one mark for reading a value correctly from the curve, with the unit from the axis
- one mark for comparing two vehicles at the same speed rather than at different speeds
- one mark for describing the shape, that stopping distance rises more steeply as speed increases
- one mark for linking the greater mass of a lorry to greater kinetic energy and so a longer braking distance
Examiner Tips
- 💡Write 'stopping distance = thinking distance + braking distance' before substituting; the equation itself often earns a mark.
- 💡Show both values you read from the graph, because later marks can still be awarded from a misread value.
- 💡Check which distance the question wants; the two words are deliberately close together in the question stem.
- 💡Quote a pair of numbers from the table when you judge a proportionality claim; the figures carry a mark of their own.
- 💡Test proportionality by dividing: if distance ÷ speed is the same for every row, it is proportional.
- 💡Use the words 'increases by a factor of four' rather than 'increases a lot'.
- 💡Write down every assumed value with its unit before you calculate; estimates are marked on the method.
- 💡Use 30 mph ≈ 13 m/s and 70 mph ≈ 31 m/s to move between road speeds and physics units.
- 💡Sanity check the answer against the typical value that a car takes about 36 m to stop from 20 m/s.
- 💡Draw the construction lines on the graph in pencil; examiners award reading marks for a visible method.
- 💡Quote both coordinates when you describe a point, for example '72 m at 30 m/s'.
- 💡When comparing vehicles, write one sentence for the similarity and one for the difference.
Common Mistakes
- quoting the braking distance alone when the question asks for the stopping distance
- saying the car is already slowing down during the thinking distance
- reading the top of a stacked bar as the braking distance, when it is the total stopping distance
- converting km/h to m/s by dividing by ten rather than by 3.6
- saying both distances double when the speed doubles
- calling the braking distance graph proportional simply because it rises as speed rises
- assuming the driver brakes harder at higher speeds, when the question fixes the braking force
- confusing the braking distance with the time taken to stop
- scaling the braking distance in direct proportion to speed instead of to its square
- using a speed in mph inside a calculation whose answer is wanted in metres
- assuming a reaction time of several seconds, well outside the typical range
- giving only the braking part and calling it the emergency stopping distance
- describing a curved stopping distance graph as directly proportional
- comparing a car at one speed with a lorry at a different speed
- misreading the axis scale when the gridlines are worth two or five units each
- saying the lorry has worse brakes rather than explaining with mass and kinetic energy