Stopping vehicles as quick as possible in an emergency is important but many factors affect this. The driver's reactions and the road and vehicle conditions play a part, as well as mass and speed.

It is important to be able to:

- estimate how the stopping distance for a vehicle varies with different speeds
- calculate the work done in bringing a moving vehicle to rest

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

Travelling at 20 mph (32 km/h):

- thinking distance = 6 m
- braking distance = 6 m
- total stopping distance = 12 m

Travelling at 40 mph (64 km/h):

- thinking distance = 12 m
- braking distance = 24 m
- total stopping distance = 36 m

Travelling at 70 mph (112 km/h):

- thinking distance = 21 m
- braking distance = 75 m
- total stopping distance = 96 m

It is important to note that the thinking distance is proportional to the starting speed. This means that it increases proportionally as speed increases - ie if speed doubles, thinking distance also doubles.

However, the braking distance increases by a factor of four each time the starting speed doubles.

For example, if a car doubles its speed from 30 mph to 60 mph, the thinking distance will double from 9 m to 18 m and the braking distance will increase by a factor of four from 14 m to 56 m.

The braking distance increases four times each time the starting speed doubles. This is because the work done in bringing a car to rest means removing all of its kinetic energy.

Work done by brakes = loss of kinetic energy

Work done = braking force × distance

This means that:

So for a fixed maximum braking force, the braking distance is proportional to the square of the velocity.

A car travels at 12 m/s. The driver has a reaction time of 0.5 s and sees a cat run into the road ahead. What is the thinking distance as the driver reacts?

distance = speed × time

The car in the previous example has a total mass of 900 kg. With a braking force of 2,000 N, what will the braking distance be?

What is the stopping distance for the car above?

stopping distance = thinking distance + braking distance

stopping distance = 6 + 32

stopping distance = 38 m

- Question
Calculate the stopping distance for the car and driver in the example above when travelling at 24 m/s.

Estimate the braking force needed to stop a family car from its top speed on a single carriageway in 100 m.

Using values of ~1,600 kg and ~27 m/s

- Question
Estimate the force needed to decelerate a lorry from its top speed on a single carriageway in 100 m.

Using values of ~36,000 kg and ~22 m/s