How is gravity related to accelerated motion?

Newton's laws of motion

Great accelerations require great forces

If a body is to be accelerated as quickly as possible (e.g. when a car starts up), correspondingly large forces must be generated.

When a car starts, the tires exert a force on the road. The corresponding reaction force of the road on the tires accelerates the car. However, this force cannot be greater than that Frictional force between tires and road.

The same applies to braking.

Since the frictional force can normally not be greater than that Normal force (this corresponds to theWeight force), the acceleration when starting and braking cannot be greater than the acceleration due to gravity g.

With the acceleration a = g, the ideal case is an acceleration from 0 to 100km / h in 2.83s and a minimum braking distance from 100km / h of 39.33m.

The fact that these values ​​are sometimes even exceeded in real cases is due to the fact that, in addition to the frictional force, other effects can play a role that can increase the reaction force.

Risk of injury in the event of an accident

In the event of an accident, vehicles are braked from high speed to a standstill within a very short time. This is only possible through very large forces that act both on the vehicle and on the occupants.

The greater the change in speed over time (i.e. the greater the braking acceleration), the greater the forces. The braking acceleration and thus the force acting on the driver depends on the speed and the braking distance. The following applies: the shorter the braking distance and the higher the speed, the higher the forces.

If a car hits a stationary object, the braking distance is just as great as the car can be deformed. This area is also known as the “crumple zone”.

In the event of an accident, it is therefore not desirable that the car is damaged as little as possible, because the forces that occur would then be even greater. Rather, efforts are made to deform as large an area as possible, which is intended to reduce the consequences of the accident on the occupants.

Calculation of the forces acting on the occupants of a car in the event of an accident:

Suppose a car is driving head-on against an obstacle at 40 km / h. The crumple zone is 80cm.

Calculation of the acceleration:

The acceleration is derived from the laws of motion

where s is the acceleration path, i.e. here the crumple zone

So you get

The braking acceleration is therefore -77.16m / s2. That corresponds to 7.9 times the acceleration due to gravity, i.e. just under 8g.


Since applies to the force , is also the force that acts on the occupants, about 8 times their weight.

This can lead to serious injuries - especially if you are not buckled up!

What is important here is the knowledge that the acceleration, and thus the force acting on the occupants, increases with the square of the speed in the event of an accident. At twice the speed (i.e. 80km / h), acceleration and force would be 4 times as large and correspond to over 31g!

How much g can a person withstand?

There is no general answer to this question because, on the one hand, the direction the occurring acceleration forces (along or across to the body axis) as well as the Duration play a major role.

People who are exposed to particularly high acceleration forces, such as fighter pilots, astronauts or racing drivers, must complete special training. Not all people are suitable for this.

For a short time (less than 0.5s) about 20g can be withstood along the body axis without any consequential damage.

You can briefly endure about 30g across your body. For a few seconds the limit is around 15g.

For roller coasters, the limit of what is allowed is 6g, astronauts have to withstand up to 5g at take-off - but then for a few minutes!