Stopping Distance (AQA 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)

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

Graph showing how the velocity typically changes as a vehicle comes to an emergency stop

• While the driver reacts (the time taken to press the brakes is called the reaction time), the vehicle continues moving at a constant velocity
  • The area underneath the graph during this time represents the thinking distance

• As soon as the brakes are applied, the vehicle decelerates to a halt
  • The area underneath the graph during this time represents the braking distance

Part (a)

Step 1: Identify the section of the graph which represents the braking distance

• • The area under a velocity-time graph represents distance travelled
  • The braking distance of the car is the distance travelled under the braking force

• • This area of the graph is shaded below:

The braking distance of the car is the area shaded because the car decelerates once the brakes are applied

Step 2: Calculate the area under the graph during the car's deceleration

• • The area is a triangle, so the braking distance is given by:

Braking distance = Area = ½ × base × height

Braking distance = ½ × (4.5 – 1) × 35 = 61.3 m

Part (b)

Step 1: Determine how long the driver takes before the brakes are applied

• • Between seeing the obstacle and applying the brakes, 1 second passes
  • This sequence of events is labelled on the graph below:

The driver's reaction time is the time between the moment they see the obstacle to the moment the brakes are applied

• • Therefore, the driver's reaction time is 1 s