Falling objects eventually reach terminal velocity – where their resultant force is zero. Stopping distances depend on speed, mass, road surface and reaction time.

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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 time varies from person to person, but is between typically 0.2 s and 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.

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

When a force is applied to the brakes of a vehicle, there is work done by the friction between the brakes and the wheel. This reduces the kinetic energy of the vehicle, slowing it down and causing the temperature of the brakes to increase.

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.

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.

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 is because the reaction time is taken as a constant, and speed = distance × time. However, the braking distance increases four times 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.