Forces and braking

Stopping distances

In an emergency, a driver must bring their vehicle to a stop in the shortest distance possible:

stopping distance = thinking distance + braking distance

This is when:

  • thinking distance is the distance a vehicle travels in the time it takes for the driver to apply the brakes after realising they need to stop
  • braking distance is the distance a vehicle travels in the time after the driver has applied the brake

Reaction times

Reaction times vary from person to person, but are typically 0.2 s to 0.9 s. A driver's reaction time can be affected by:

Longer reaction times increase the thinking distance when stopping from a given speed.

There are different ways to measure reaction times. One simple method involves dropping a ruler between someone's open thumb and forefinger. The higher the reaction time needed to grasp the falling ruler, the further the ruler falls before being stopped.

Braking distance

The braking distance of a vehicle can be affected by:

  • poor road and weather conditions, such as wet or icy roads
  • poor vehicle conditions, such as worn brakes or worn tyres

The faster a vehicle travels, the greater the braking force needed to stop it in a certain distance. A greater braking force produces a greater deceleration. Large decelerations may cause the brakes to overheat, and the driver may also lose control of the vehicle.

Typical stopping distances

It is important to be able to:

  • estimate how the stopping distance for a vehicle varies with different speeds
  • interpret graphs relating speed to stopping distance

The diagram shows some typical stopping distances for an average car in normal conditions.

Bar chart showing the thinking and braking distances of a car at different speeds. The greater the speed, the longer the thinking and braking takes.

It is important to note that the thinking distance is proportional to the starting speed. This is because the reaction time is taken as a constant, and speed = distance × time. However, the braking distance increases by a factor of four each time the starting speed doubles.

Car safety features

Car safety features such as seatbelts, airbags and crumple zones all work to change the shape of the car, which increases the time taken for the collision. Crumple zones refer to the areas of a car that are designed to deform or crumple on impact. These different safety features decrease the force of the collision on any people within the car.

Side view of a crashed car, showing the crumple zones and activated airbags.

Explaining car safety features - Higher

During a collision there is a change in momentum. The force of the collision is equal to the rate of change of momentum. The safety features decrease the rate of change of momentum, which decreases the force of the collision on any people within the car.

Effects of rapid deceleration

When cars are involved in accidents, the forces exerted are very large. Crumple zones are designed to increase the time it takes for a car to stop totally. This reduces the force acting on a car. Seat belts and air bags are designed to increase the time it takes for passengers in a car to stop totally. This reduces the force acting on the passengers.

Example calculation - Higher

Consider two cars colliding.

The mass of each car is 1,000 kg and they are both travelling at 20 m/s (72 km/h).

Because momentum is conserved, they are both stationary after the impact.

average velocity = (20 + 0) ÷ 2 = 10 m/s

During a collision, the crumple zone is shortened by 0.50 m.

Using the equation:

average~velocity = \frac{distance}{time}

time = \frac{distance}{average~velocity} = \frac{0.50}{10} = 0.05~s

F = \frac{m \Delta v}{\Delta t} = \frac{1,000 \times 20}{0.05} = 400,000~N

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