Reaction times, stopping distances and road safety

1. One person holds a 30 cm ruler vertically. The person being tested places their open thumb and finger around its lower end without touching it. Align the zero mark with the catching position.
2. Release the ruler without warning, so the person cannot simply anticipate the release.
3. The person closes their thumb and finger as soon as they see the ruler fall.
4. Read the distance fallen at the catching position. A greater distance means a longer reaction time.
5. Repeat several times to check how consistent the results are. When comparing people or conditions, keep the starting position and release method the same.

The ruler measures distance directly, rather than time in seconds. Its falling distance can be converted into a reaction time, but that conversion is not needed to understand this test. A missed catch should be recorded as a missed catch, not as a distance measured beyond the ruler's scale.

The two parts of stopping distance

A vehicle's stopping distance is the total distance travelled from the driver noticing a hazard until the vehicle comes to rest. It has two distinct parts.

During the thinking distance, the driver is reacting and has not yet applied the brakes. During the braking distance, the brakes are acting and the vehicle slows down.

$$\text{stopping distance}=\text{thinking distance}+\text{braking distance}$$

For example, if a vehicle travels 14 m while the driver reacts and its total stopping distance is 40 m, its braking distance is $40-14=26\text{ m}$. The two distances describe consecutive stages of the same stop.

What makes thinking distance longer?

If the vehicle's speed remains approximately constant while the driver reacts:

$$\text{thinking distance}=\text{speed}\times\text{reaction time}$$

Use speed in metres per second and reaction time in seconds to obtain distance in metres. For a fixed reaction time, doubling the speed doubles the thinking distance: the vehicle travels twice as far during the same delay.

A longer reaction time also increases thinking distance at the same speed. Important causes include:

• Tiredness, which makes the driver slower to respond.
• Alcohol and other drugs, which can impair the driver's responses.
• Distractions, such as using a mobile phone, which divert attention from the road.

These factors act before braking begins. Better brakes cannot remove the distance already travelled while the driver is reacting.

What makes braking distance longer?

Brakes produce friction that slows the wheels, while friction between the tyres and the road provides the grip needed to slow the vehicle. Braking transfers the vehicle's kinetic energy, the energy it has because it is moving, mainly into thermal energy.

Higher speed increases braking distance. At the same mass, a faster vehicle has more kinetic energy to transfer before stopping. If the braking force stays constant, braking distance is proportional to speed squared: doubling the speed makes braking distance four times as large. This differs from thinking distance, which only doubles for the same reaction time.

Greater vehicle mass also increases braking distance for the same braking force. A larger mass needs a greater force to produce the same deceleration. If the force does not increase, the vehicle slows less rapidly and travels farther before stopping.

Poor brake condition can reduce the effective braking force, increasing braking distance. Brakes also heat up during use; if they become too hot, they can become less effective or fail.

Wet or icy roads reduce friction between the tyres and the road. With less grip, the vehicle cannot decelerate as effectively, so braking distance increases. Worn tyres can also reduce grip, particularly in wet conditions.

Road state and tyre condition are therefore connected through tyre–road friction. They do not change the driver's reaction time, but they can make the braking stage much longer. Several adverse factors can act together: a tired driver travelling quickly on an icy road has both an increased thinking distance and an increased braking distance.

Why large decelerations are dangerous — Higher tier

Deceleration means a decrease in speed. A rapid stop produces a large deceleration, which requires a large resultant force:

$$F=ma$$

Here, $F$ is resultant force in newtons, $m$ is mass in kilograms and $a$ is acceleration in metres per second squared. To estimate the average acceleration during a stop, use:

$$a=\frac{v-u}{t}$$

Here, $u$ is initial velocity, $v$ is final velocity and $t$ is the stopping time. For the same change in velocity, a shorter stopping time means a larger deceleration and a larger force.

Consider a road collision in which a passenger travelling at about 20 m/s comes to rest in 0.1 s. Take the passenger's mass as about 70 kg. Choosing the original direction of travel as positive gives:

$$a=\frac{0-20}{0.1}=-200\text{ m/s}^2$$

The estimated average resultant force on the passenger is:

$$F=70\times(-200)=-14\,000\text{ N}$$

The force has a magnitude of about 14,000 N and acts opposite to the passenger's original motion. These are estimates, not exact values for every collision. They show why bringing a person to rest in a very short time can cause serious injury.

Sudden movement of the head relative to the body can cause a neck injury called whiplash. Severe braking can also make a vehicle harder to control, especially when grip is poor, increasing the risk of a collision.

• Thinking distance: increases with speed or reaction time.
• Braking distance: increases with speed, greater mass for the same braking force, ineffective brakes, worn tyres, or reduced grip on wet or icy roads.
• Doubling speed doubles thinking distance at fixed reaction time, but quadruples braking distance at fixed mass and braking force.

Large decelerations — Higher tier

$$a=\frac{v-u}{t},\qquad F=ma$$

• Shorter stopping time for the same velocity change → greater deceleration → greater force.
• Large forces can injure occupants; sudden head movement can cause whiplash.
• Severe braking can cause loss of control. Overheated brakes can become ineffective.