AQA GCSE Combined Science (8464), Higher tier · Physics › Forces › Forces and motion › Forces and braking
Practise Stopping distance. 16 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
The stopping distance of a vehicle is the thinking distance plus the braking distance. You need to know what affects each part, how speed affects stopping distance, and how to calculate stopping distances from data. GCSE Physics also asks you to interpret graphs of stopping distance against speed for different vehicles.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
State that stopping distance = thinking + braking distanceThinking distance is covered during the reaction time; braking distance is covered while the brakes act.
4
Calculate stopping distance from given dataAdd the thinking distance and the braking distance.
5
Calculate thinking distance using s = v tThinking distance = speed × reaction time.
6
Explain how speed affects stopping distanceFor a given braking force, a greater speed gives a greater thinking distance and a greater braking distance.
7
Interpret stopping distance data and graphsThinking distance rises in proportion to speed; braking distance rises more and more steeply.
8
Explain why braking distance increases fastestFor the same braking force, braking distance is proportional to speed squared, because kinetic energy is.
Thinking distance: the distance the vehicle travels during the driver's reaction time, between seeing a hazard and applying the brakes.
Braking distance: the distance the vehicle travels under the braking force, from applying the brakes until it stops.
The effect of speed
For a given braking force, the greater the speed of the vehicle, the greater the stopping distance.
Thinking distance = speed × reaction time. For the same reaction time, thinking distance is directly proportional to speed: double the speed, double the thinking distance.
The work done by the brakes (braking force × braking distance) equals the kinetic energy (½ m v2). So for the same braking force, braking distance is proportional to speed2: double the speed, four times the braking distance. grade 8+
So at higher speeds, the braking distance makes up a bigger share of the stopping distance.
What affects each part
Thinking distance depends on the speed and on the driver's reaction time, which is increased by tiredness, drugs, alcohol and distractions.
Braking distance depends on the speed, the road and weather conditions (wet or icy), the condition of the brakes and tyres, and the mass of the vehicle.
Thinking distance: the car travels further during the reaction time.
Braking distance: more kinetic energy, so more work must be done by the brakes.
So the total stopping distance increases.
Example. Explain why a car travelling at a higher speed has a longer stopping distance, for the same braking force.
Show the model answer
At a higher speed the car travels further during the driver's reaction time, so the thinking distance is greater (1). The car has more kinetic energy, so more work must be done by the brakes and the braking distance is greater (1). Stopping distance = thinking distance + braking distance, so it increases (1).
Evaluate a statement using data
3 marks7
Calculate the values the statement is about.
Compare them and say whether the statement is right.
Explain using the separate thinking and braking distances.
Example. Data for a car: at 10 m/s, thinking distance 7 m and braking distance 8 m; at 20 m/s, thinking distance 14 m and braking distance 32 m. A student says: 'Doubling the speed doubles the stopping distance.' Use the data to evaluate this statement.
Show the model answer
Stopping distance at 10 m/s = 15 m; at 20 m/s = 46 m (1). 46 m is about three times 15 m, so the statement is wrong (1). The thinking distance doubles (7 m to 14 m), but the braking distance is four times bigger (8 m to 32 m) (1).
A driver sees a fallen tree 55 m ahead and makes an emergency stop. The car is travelling at 22 m/s. The driver’s reaction time is 0.65 s. When the brakes are applied, the car decelerates uniformly at 7.0 m/s2.
(a) Calculate the thinking distance.[2]
(b) Calculate the braking distance. Use the Physics Equations Sheet.[3]
(c) Determine whether the car stops before it reaches the tree.[1]
(d) On another day the driver is tired and has a reaction time of 1.2 s. The car travels at the same speed and decelerates at the same rate. Show that the car would not stop before reaching the tree.[3]
Show the answer and mark scheme
(a)Answer: 14.3 m
s = 22 × 0.65
14.3 (m)
(b)Answer: 34.6 m
0 − 222 = 2 × (−7.0) × s
s = 484 ÷ 14
34.6 (m)
(c)Answer: Yes: the stopping distance is 48.9 m, which is less than 55 m.
stopping distance = 48.9 m, which is less than 55 m, so the car stops (6.1 m) before the tree
(d)Answer: Thinking distance 26.4 m + braking distance 34.6 m = 61.0 m, which is more than 55 m.
thinking distance = 22 × 1.2 = 26.4 (m)
stopping distance = 26.4 + 34.6 = 61.0 (m)
61.0 m is greater than 55 m, so the car does not stop in time