# 5.8.1 Thinking & Braking Distances

### Thinking & Braking Distances

• The stopping distance of a car is defined as:

The total distance travelled during the time it takes for a car to stop in response to some emergency

• It can be written as an equation involving two distances:

Stopping distance = Thinking distance + Braking distance

• Where:
• Thinking distance = the distance travelled in the time it takes the driver to react (reaction time) in metres (m)
• Braking distance = the distance travelled under the braking force in metres (m)
• Stopping distance = the sum of the thinking distance and braking distance, in metres (m)
• For a given braking force, the greater the speed of the vehicle, the greater the stopping distance

#### Worked Example

At a speed of 20 m/s, a particular vehicle had a stopping distance of 40 metres. The car travelled 14 metres whilst the driver was reacting to the incident in front of him. What was the braking distance?

A      54 m

B      34 m

C      26 m

D      6 m

Step 1: Identify the different variables

• Stopping distance = 40 m
• Thinking distance = 14 m

Step 2: Rearrange the formula for stopping distance

Stopping distance = Thinking distance + Braking distance

Braking distance = Stopping distance – Thinking distance

Step 3: Calculate and identify the correct braking distance

• Braking distance = 40 – 14 = 26 metres
• Therefore, the answer is C

### 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.
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