Braking & Reaction Times (OCR A Level Physics)

• The stopping distance of a car is the distance it travels in the time it takes to stop in response to an emergency
• The stopping distance consists of two parts:
  • The thinking distance
  • The braking distance

• Therefore, the stopping distance is equal to:

Stopping distance = Thinking distance + Braking distance

• The graph below shows how the velocity of a car will typically change during an emergency stop

A velocity-time graph for a stopping car showing thinking and braking distance

• The stopping distance increases considerably with the speed of a car
  • This is mostly because a car will travel further whilst braking before coming to rest

Estimate of stopping distances for various speeds

• The image illustrates the following important principles:
  • The thinking distance increases proportionally with speed (i.e. if speed doubles, the thinking distance doubles)
  • The braking distance increases at an even faster rate with speed

• For a typical family car, these speeds and stopping distances are summarised in the table below:

Table of Stopping Distances for a Family Car

Thinking Distance

• Thinking distance is defined as:

The distance travelled by the vehicle from when the driver sees a problem and the brakes are applied

• The thinking distance is proportional to the initial speed, u, of the vehicle
• The thinking distance can be calculated from:

Thinking distance = Initial speed × Reaction time

• Where:
  • Reaction time =  the time taken by the driver to respond to the problem

• Factors that affect thinking distance are:
  • The initial speed of the vehicle
  • Intoxication ie. consumption of alcohol or drugs
  • Distractions ie. using a mobile phone
  • Tiredness (since reaction times increase when tired)

Braking Distance

• Braking distance is defined as:

The distance travelled by the vehicle after the driver has applied the brake

• The braking distance of the vehicle is proportional to the square of the initial speed of the car, u²
• This is because all of the vehicle’s kinetic energy (½ mv²) must be dissipated by the brakes in order to come to a stop
• The work done by the brakes is given by:

Work Done = Braking Force × Braking Distance = ½ mv²

• Factors that affect braking distance are:
  • The initial speed of the vehicle
  • Mass of the vehicle
  • Poor road conditions eg. icy, wet
  • Car conditions eg. worn brakes