Section 1 of 6Stopping Distance Equation
Thinking distance
- The distance travelled while the driver reacts, found by multiplying the speed by the reaction time.
Braking distance
- The distance the car travels after the brakes are applied until it stops, which depends on speed and braking force.
Stopping distance
- The total distance to stop, equal to thinking distance plus braking distance.
Speed link
- Thinking distance grows in direct proportion to speed, while braking distance grows much faster than the speed.
| Speed (m/s) | Typical thinking distance (m) | Typical braking distance (m) |
|---|---|---|
| 10 | about 7 | about 10 |
| 20 | about 14 | about 40 |
| 30 | about 21 | about 90 |
Section 2 of 6Calculating Each Part
1
Calculate the thinking distance from the speed and the reaction time using distance = speed × time.
2
Find the deceleration during braking from the change in speed, using v² = u² + 2as with the final speed v equal to zero.
3
Use F = ma to convert the deceleration into the braking force, or use work done by the brakes equal to kinetic energy lost.
4
Add the thinking distance and the braking distance to obtain the stopping distance, and quote the unit metres.
5
Check that the answer is sensible: a car at 20 m/s should need tens of metres to stop, not thousands.
Section 3 of 6Why Large Decelerations Are Dangerous
Why Large Decelerations Are Dangerous
Large force
- For a given mass a bigger deceleration needs a bigger braking force, because F = ma links the two quantities.
Brake overheating
- The brakes change kinetic energy into thermal energy, so very rapid stopping can heat them until they stop working well.
Loss of control
- If the braking force exceeds the friction between tyre and road, the wheels skid and the car cannot be steered properly.
Injury
- A sudden stop requires a large force on the passengers, which can cause injury if they are not restrained by seat belts.
Section 4 of 6Factors That Change the Result
Reaction time
- Tiredness, alcohol, drugs and distractions raise reaction time, which lengthens the thinking distance.
Speed
- Kinetic energy depends on the square of speed, so doubling speed makes the braking distance about four times as long.
Road conditions
- Wet, icy or loose surfaces reduce friction, so for the same brake force the braking distance becomes longer.
Vehicle condition
- Worn brakes and worn tyres give a smaller braking force, increasing braking distance.
Section 5 of 6Worked Example
Question
- A car of mass 1200 kg travels at 20 m/s.
- The driver's reaction time is 0.70 s and the car stops in a braking distance of 40 m.
- Calculate the stopping distance and the average braking force.
- Thinking distance = 20 × 0.70 = 14 m.
- Deceleration from v² = u² + 2as: 0 = 400 + 2 × a × 40, so a = −5.0 m/s² (a deceleration of 5.0 m/s²).
- Force F = ma = 1200 × 5.0 = 6000 N; stopping distance = 14 + 40 = 54 m.
Answer The stopping distance is 54 m and the average braking force is 6000 N.
Section 6 of 6Exam Checklist & Tips
2.4.4 – Key Points for the Exam
- Stopping distance The total distance travelled between the driver seeing a hazard and the vehicle coming to rest.
- Thinking distance The distance travelled during the driver's reaction time, before the brakes are used.
- Braking distance The distance travelled while the brakes are slowing the vehicle to a stop.
- Deceleration A negative acceleration, meaning the object is slowing down.
- Reaction time The time between a stimulus appearing and the person responding to it.
Common Mistakes
- Using the stopping distance as if it only included braking; the thinking distance must be added.
- Assuming braking distance doubles when speed doubles; it increases roughly four times.
- Leaving a deceleration as a positive number in v² = u² + 2as when the car is slowing down.
- Mixing units, for example using speed in km/h with a time in seconds in the same equation.