# 5.8.2 Stopping Distance

### Estimating Stopping Distances

• 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 Open Government License)

• 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 ### Graphs Relating Speed to Stopping Distance

• 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

#### Worked Example

While driving at a speed of 35 m/s, Stephen sees an obstacle in the road at time t = 0.

The velocity-time graph below shows how the speed of the car changes as Stephen reacts and slams the brakes, bringing the car to a halt. Determine

(a) The braking distance of the car.

(b) The driver’s reaction time.

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 ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
Close Close