Section 1 of 9Stopping distance
When a driver sees a hazard the car does not stop at once. The total stopping distance is the sum of two parts:
stopping distance = thinking distance + braking distance
The thinking distance is how far the car travels during the driver's reaction time, before the brakes are applied. The braking distance is how far it travels while the brakes are slowing it down.
Section 2 of 9Thinking distance
During the reaction time the car moves at its original speed, so thinking distance = speed × reaction time. It is directly proportional to speed: doubling the speed doubles the thinking distance. Typical reaction times are 0.2 s to 0.9 s. The thinking distance increases when the driver is:
- tired,
- distracted (for example by a phone),
- under the influence of alcohol or some drugs,
- driving faster.
Reaction time can be measured by a ruler-drop test.
Section 3 of 9Braking distance
The braking force does work against the car's kinetic energy. The work done by the brakes equals the force times the braking distance, so braking force × distance = ½mv2 (Supplement). Because of the v2, doubling the speed makes the braking distance four times longer, at the same braking force.
Braking distance increases when:
The same facts explain why a loaded lorry needs more space to stop: more mass means more kinetic energy to remove, so the braking distance increases if the braking force is unchanged.
Section 4 of 9Safety and deceleration
A large braking force produces a large deceleration, which can cause skidding and large forces on passengers. Anti-lock braking systems pulse the brakes to avoid skidding on slippery roads. Seat belts and speed limits in towns reduce the damage of collisions.
The deceleration is related to the braking force by F = ma. For a given car and a safe braking force, a larger deceleration means a smaller braking distance but a greater force on the passengers, and a bigger risk of skidding. Road safety design tries to give enough friction without causing harm during the stop.
Section 5 of 9Graphs
A speed–time graph of a stopping car is flat during the thinking time (constant speed), then falls in a straight line during braking. The area under the flat part is the thinking distance, and the area under the sloping part is the braking distance. The total area is the stopping distance.
A graph of braking distance against speed is a curve that gets steeper; thinking distance against speed is a straight line through the origin.
Section 6 of 9Putting numbers together
At 30 mph (about 13 m/s) total stopping distance is about 23 m. At 60 mph it is about 73 m, more than three times as much. This is why speed limits are lower near schools.
Exam questions often give a table of thinking and braking distances at several speeds and ask what happens when speed is doubled.
- but if the braking distance goes from 6 m to 24 m, it is a square relationship.
Section 7 of 9Worked examples
A driver with a reaction time of 0.70 s travels at 20 m/s. Find the thinking distance.
d = vt = 20 × 0.70 = 14 m.
A car travelling at 15 m/s has a braking distance of 20 m. Estimate the braking distance at 30 m/s with the same brakes.
Speed doubles, so braking distance increases by 22 = 4: 20 × 4 = 80 m.
The thinking distance of a driver at 25 m/s is 15 m, and the braking distance is 38 m. Find the stopping distance and the reaction time.
Stopping distance = 15 + 38 = 53 m.
t = d/v = 15/25 = 0.60 s.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Thinking distance | Distance travelled in the driver's reaction time. |
| Braking distance | Distance travelled while the brakes slow the vehicle. |
| Reaction time | Time between seeing a hazard and applying brakes. |
| Stopping distance | Thinking distance plus braking distance. |
| Friction | Force between tyres and road that allows braking. |