The formula used to calculate braking distance can be derived from a general equation of physics:
where “Vf” is the final velocity, “V0” is the initial velocity, “a” is the rate of deceleration and “d” is the distance travelled during deceleration. Since we know that “Vf” will be zero when the car has stopped, this equation can be re-written as:
From this we can see that braking distance is proportional to the square of the speed – which means that it increases considerably as speed increases. If we assume that a is 10 metres per second and assume that the road is flat and the braking systems of the two cars are equally effective, we can now calculate braking distance for cars 1 and 2 in our example. For car 1, d = 16.3 metres, while for Car 2, d = 13.9 metres.
Adding reaction distance to braking distance, the stopping distance for Car 1 is 27.1 + 16.3 = 43.4 metres. For Car 2, stopping distance is 25 + 13.9 = 38.9 metres. Car 1 therefore takes 4.5 more metres to stop than Car 2, a 12 per cent increase.
We can now see why Car 1 is more likely than Car 2 to hit Sam. If Sam is 40 metres from the cars when the drivers see him, Car 2 will stop just in time. Car 1, though, will plough straight into him. By re-writing the first equation, we can calculate the speed at which the collision occurs:
(where d = 40 metres minus the reaction distance of 27.1 metres = 12.9 metres).
Thus, the impact occurs at about 30 kilometres/hour, probably fast enough to kill the child. If the car’s initial speed were 70 kilometres/hour the impact velocity would be 45 kilometres/hour, more than fast enough to kill.
Impact on a pedestrian
Because the pedestrian, a child, is so much lighter than the car, he has little effect upon its speed. The car, however, very rapidly increases the child’s speed from zero to the impact speed of the vehicle. The time taken for this is about the time it takes for the car to travel a distance equal to the child’s thickness – about 20 centimetres. The impact speed of Car 1 in our example is about 8.1 metres per second, so the impact lasts only about 0.025 seconds. The child must be accelerated at a rate of about 320 ms-2 during this short time. If the child weighs 50 kilograms, then the force required is the product of his mass and his acceleration – about 16,000 .
Since the impact force on the child depends on the impact speed divided by the impact time, it increases as the square of the impact speed. The impact speed, as we have seen above, increases rapidly as the travel speed increases, because the brakes are unable to bring the car to a stop in time.
Impact on a large object
If, instead of hitting a pedestrian, the car hits a tree, a brick wall, or some other heavy object, then the car's energy of motion () is all dissipated when the car body is bent and smashed. Since the kinetic energy (E) is given by
E = (1/2) mass × speed2
it increases as the square of the impact velocity. Driving a very heavy vehicle does not lessen the effect of the impact much because, although there is more metal to absorb the impact energy, there is also more energy to be absorbed.
Less control
At higher speeds cars become more difficult to manoeuvre, a fact partly explained by Newton’s First Law of Motion. This states that if the net force acting on an object is zero then the object will either remain at rest or continue to move in a straight line with no change in speed. This resistance of an object to changing its state of rest or motion is called inertia. It is inertia that will keep you moving when the car you are in comes to a sudden stop (unless you are restrained by a seatbelt).
To counteract inertia when navigating a bend in the road we need to apply a force – which we do by turning the steering wheel to change the direction of the tyres. This makes the car deviate from the straight line in which it is travelling and go round the bend. The force between the tyres and the road increases with increasing speed and with the sharpness of the turn (Force = mass × velocity squared, divided by the radius of the turn), increasing the likelihood of an uncontrolled skid. High speed also increases the potential for driver error caused by over- or under-steering (turning the steering wheel too far, thereby ‘cutting the corner’, or not far enough, so that the car hits the outside shoulder of the road).
Killer speed
All these factors show that the risk of being involved in a casualty crash increases dramatically with increasing speed.
Is the risk worth it? In our hypothetical case, the driver of Car 2, travelling at the speed limit, would have had a nasty scare, but nothing more. The driver of Car 1, driving just 5 kilometres/hour above the limit, would not be so lucky: whether the child had lived or died, he or she would face legal proceedings, a possible jail sentence, and a whole lifetime of guilt.
