It might seem inconsequential, but increasing your driving speed even slightly above the posted limit significantly elevates your risk of being involved in a car accident. Many drivers are tempted to exceed speed limits by a small margin, assuming it’s harmless as long as it’s just a few kilometers per hour over. However, this seemingly minor increase dramatically affects how quickly a car can stop and substantially increases the likelihood of a crash.
Research from the University of Adelaide, analyzing real-world crash data, has quantified the heightened risk. Their study on the relative risk of casualty crashes for vehicles traveling at or above 60 km/h revealed a startling trend: for every 5 km/h increment over 60 km/h, the risk of a casualty crash – one resulting in serious injury or fatality – roughly doubles. This means a car moving at 65 km/h is twice as likely to be involved in a severe accident compared to one traveling at 60 km/h. At 70 km/h, this risk quadruples. Conversely, driving below 60 km/h is expected to reduce the chance of a fatal crash.
Small adjustments in speed and driver attentiveness can have a profound impact on a vehicle’s stopping distance, highlighting How Quickly A Car Stops Depends On various factors.
Interactive stopping distance calculator tools can illustrate this point effectively.
Alt text: Blue car depicted in a stopping distance calculator interface, emphasizing the role of speed in calculating total stopping distance.
The Physics Behind Stopping: Reaction Time and Braking Distance
Why does even a small increase in speed so dramatically affect accident risk? The answer lies in physics, specifically in reaction time and braking distance.
Reaction Time: The First Component of Stopping Distance
Reaction time is the interval between a driver recognizing a hazard and initiating a response, such as applying the brakes. To illustrate, consider two identical cars with equal braking capabilities. Car 1 travels at 65 km/h, overtaking Car 2 at 60 km/h. Suddenly, a child on a bicycle, named Sam, enters the road from a driveway just as the cars are side-by-side. Both drivers spot Sam simultaneously and take an average reaction time of 1.5 seconds to fully engage their brakes. During this reaction period, Car 1 covers 27.1 meters, while Car 2 travels 25.0 meters.
Alt text: Visual representation of reaction time in car stopping distance, showing distance covered during driver’s reaction at different speeds.
This seemingly small 2.1-meter difference in reaction distance can be critical, potentially determining whether Sam is safe or injured. It’s important to note that 1.5 seconds is considered an average reaction time. Factors like driver distraction – caused by loud music, phone use, or alcohol – can significantly lengthen reaction times, sometimes to 3 seconds or more. Increased reaction time directly increases the distance covered before braking even begins, thus increasing the overall distance required to stop a car.
Braking Distance: The Second Component Influenced by Speed
Braking distance is the distance a car travels after the brakes are applied until it comes to a complete stop. Several factors influence braking distance. Roadway slope is a significant factor; a car going uphill will stop more quickly due to gravity assistance. Friction between tires and the road surface also plays a crucial role. New tires on dry pavement provide superior grip and will result in shorter braking distances compared to worn tires on wet roads, which are more prone to skidding. However, when considering similar road conditions and vehicle conditions, initial speed becomes the most dominant factor affecting braking distance.
The physics formula governing braking distance is derived from the equation of motion:
$$V_{f}^{2} = V_{0}^{2} – 2ad$$
Where:
- (V_f) is the final velocity (0 m/s when stopped).
- (V_0) is the initial velocity.
- (a) is deceleration rate.
- (d) is braking distance.
This equation can be rearranged to solve for braking distance (d):
$$d = V_{0}^{2} / 2a$$
This formula clearly demonstrates that braking distance is proportional to the square of the initial speed. This square relationship means that even small increases in speed lead to substantial increases in braking distance.
Assuming a deceleration rate (a) of 10 m/s² and identical flat road and braking systems for Car 1 and Car 2, we can calculate their braking distances. For Car 1 (65 km/h), braking distance is approximately 16.3 meters, while for Car 2 (60 km/h), it’s about 13.9 meters.
Total Stopping Distance: Reaction Distance Plus Braking Distance
Total stopping distance is the sum of reaction distance and braking distance. For Car 1, it’s 27.1 meters (reaction) + 16.3 meters (braking) = 43.4 meters. For Car 2, it’s 25.0 meters (reaction) + 13.9 meters (braking) = 38.9 meters. Therefore, Car 1 requires 4.5 meters more to stop than Car 2 – a 12% increase in stopping distance due to a slight speed difference.
Alt text: Diagram illustrating stopping time and distance, visually comparing reaction distance and braking distance components.
This difference can be life-saving. If Sam is 40 meters away when the drivers react, Car 2 will stop just in time. However, Car 1 will collide with Sam. By recalculating the velocity at impact using the equation:
$$V_{f} = sqrt{V_{0}^{2} – 2ad}$$
(where d = 40 meters – 27.1 meters (reaction distance) = 12.9 meters), we find the impact speed of Car 1 is approximately 8.2 m/s, or about 30 km/h. An impact at 30 km/h is highly likely to cause fatal injuries to a pedestrian. If Car 1 had been traveling at 70 km/h initially, the impact speed would increase to around 45 km/h, making a fatality even more certain.
These calculations assume average driver reaction times. Distracted drivers with longer reaction times might not even begin braking before hitting Sam.
Impact Speed and Consequences: Pedestrians and Objects
The consequences of impact are severe, especially for vulnerable road users like pedestrians.
Impact on a Pedestrian
Due to the significant weight disparity between a car and a pedestrian, the car’s speed is minimally affected upon impact. However, the pedestrian is violently accelerated from standstill to the car’s impact speed in a fraction of a second – roughly the time it takes for the car to travel a distance equal to the pedestrian’s thickness (around 20 cm). In our example, Car 1’s impact speed of 8.2 m/s results in an impact duration of just 0.024 seconds, requiring Sam to accelerate at an astonishing 320 m/s². For a 50kg person, this translates to an impact force of about 16,000 Newtons, or roughly 1.6 tonnes of weight.
Crucially, the impact force on a pedestrian increases with the square of the impact speed. Reducing impact speed significantly reduces the severity of injuries. Lowering the impact speed from 60 km/h to 50 km/h nearly halves the probability of pedestrian fatality, while reducing speed to 40 km/h, as commonly implemented in school zones, reduces fatality risk by a factor of four compared to 60 km/h.
Alt text: Graphic depicting pedestrian impact scenario, highlighting the severe consequences of vehicle speed on pedestrian safety.
Vehicle design also plays a role. Modern cars with lower, streamlined hoods are generally more pedestrian-friendly compared to upright designs, like those of SUVs, as they tend to throw pedestrians upwards onto the windshield, potentially reducing the severity of the initial impact. Conversely, bull bars on vehicles are particularly dangerous for pedestrians and other vehicles, prioritizing occupant protection with little regard for others.
Impact on a Large Object
When a car collides with a solid, immovable object like a tree or wall, all its kinetic energy is dissipated through vehicle deformation and damage. Kinetic energy (E) is calculated as:
$$E = (1/2) × mass × speed^{2}$$
Like braking distance and impact force, kinetic energy also increases with the square of the speed. Heavier vehicles don’t significantly lessen impact severity because, while they might have more structural mass to absorb energy, they also possess greater kinetic energy at the same speed.
Reduced Control at Higher Speeds
Newton’s First Law of Motion, the principle of inertia, explains another critical way speed diminishes safety. Inertia is an object’s resistance to changes in its motion.
GLOSSARY
inertia: the resistance of any physical object to any change in its state of motion, including changes to its speed and direction. It is the tendency of objects to keep moving in a straight line at constant velocity.
When navigating a curve, overcoming inertia requires applying force by steering. This force, generated through tire-road friction, must counteract the car’s tendency to continue straight. The force needed increases dramatically with speed and curve sharpness (Force = mass × velocity² / radius of turn). Exceeding the tire’s grip limit leads to skidding and loss of control. Higher speeds also amplify driver errors like oversteering or understeering, further increasing accident risk.
Speed: A Killer Factor
The evidence is clear: the risk of a casualty crash escalates sharply with increased speed. The University of Adelaide research confirmed this in 60 km/h speed limit zones, where accident risk doubled for every 5 km/h above the limit. This principle extends to lower speed limit zones as well.
You decide on your speed, but physics decides whether you live or die. TAC Road Safety Commercial
Conclusion: Is Speeding Worth the Risk?
Consider our example again. The driver of Car 2, adhering to the speed limit, would have experienced a close call but avoided an accident. However, the driver of Car 1, exceeding the limit by a mere 5 km/h, would have faced devastating consequences – potential legal charges, possible imprisonment, and the lifelong burden of guilt, regardless of Sam’s fate. Understanding how quickly a car stops depends on speed and other factors is not just a matter of physics; it’s a matter of life and death.
See our infographic on Australian road statistics.
