It is important to be able to:
The diagram shows some typical stopping distances for an average car in normal conditions.
Travelling at 20 mph (32 km/h):
Travelling at 40 mph (64 km/h):
Travelling at 70 mph (112 km/h):
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
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
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