Calculating Stopping Distances (Edexcel GCSE Physics)

• For a given braking force, the speed of a vehicle determines the size of the stopping distance
• The greater the speed of the vehicle, the larger the stopping distance
• The image below shows how the stopping distance of a typical family car increases with increasing speed:

A vehicle's stopping distance increases with speed. At a speed of 20 mph the stopping distance is 12 m, whereas at 60 mph the stopping distance is 73 m (reproduced from the UK Highway Code under the

Step 1: Identify the variables

• • The diagram contains information for a car at a velocity of 50 mph as follows:
  • Thinking distance = 15 m
  • Braking distance = 38 m
  • Stopping distance = 53 m
  • The new speed is 100 mph which is double the velocity in the diagram

Step 2: State the relationship between thinking and braking distance, and velocity

• • Thinking distance is proportional to the velocity
  • Braking distance is proportional to the velocity squared

Step 3: Calculate the new thinking and braking distances

• • Thinking distance at 100 mph = 15 × 2 = 30 m
  • Braking distance at 100 mph = 38 × 4 = 152 m

Step 4: Calculate the new stopping distance

• • Stopping distance = Thinking distance + Braking distance
  • Stopping distance = 30 + 152 = 182 m

• When a vehicle stops work is done by a force
• The kinetic energy of the car is transferred to thermal energy in the brakes which does work
• This can also be represented by the braking force and braking distance by the following equation:

• This equation shows that the work done is the transfer of kinetic energy
• We can use this equation to estimate the decelerating forces required for a typical vehicle moving at everyday speeds

• This equation can be rearranged to show how the braking distance depends on velocity:

Equation for braking distance from mass, velocity and braking force

• The braking distance is proportional to the vehicle's velocity squared
  • For example, if the velocity of the vehicle doubles then the braking distance will increase by a factor of 4