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School Physics: Forces & motion 5.2 Calculating stopping distances from graph

GCSE level Physics exam revision notes on Forces & Motion Part 5

Part 5.2 Road safety - How to calculate thinking, braking & stopping distances from velocity - time graphs for road vehicles

[Author © Dr Phil Brown PhD: Doc Brown's physics exam revision notes suitable for students of UK IGCSE & GCSE level physics courses, ~ US grades 9-10 physics [forces-motion-5- updated Mar 26th 2026]

[KEY POINTS and learning objectives for this page, after initial notes]

See parts 5.5, .6 and 5.8 via index link below

INDEX of physics notes: reaction times, stopping distances of road vehicles, Newton's 2nd Law, KE calculations

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5.2 How to calculate thinking distances and braking distances from velocity - time graphs

From the graph areas:

A1 + A2 = thinking distance + braking distance = total area = stopping distance

A2 is the actual deceleration area.

You have probably encountered velocity time graphs by now, so you should know that the area under a section of a velocity- time graph is equal to the distance travelled in that section (in terms of units m/s x s = m).

The graphs assume the same car and driver so that the deceleration on maximum braking is the same, which is why the negative gradient is the same value on both graphs.

 

The graph on the left of 1a shows an initial situation of a driver's quicker response time travelling at a lower speed.

Rectangular area A1 = initial velocity v1 x reaction time t1 = thinking distance

The area A1 is equal to the thinking distance, that is the distance the vehicle travels in the time it takes the driver to respond to a situation and starts to apply the brakes.

Right angled triangular area A2 = ˝  x initial velocity v1 x braking time t2 = braking distance

The area A2 is the braking distance, that is the distance the vehicle travels from its maximum initial speed, when braking starts, until it comes to a halt.

The total area = A1 + A2 = stopping distance

 

The graph on the right of 1a shows a driver's slower reaction and the vehicle is moving at a greater speed.

This means two factors have been changed to emphasise how stopping distance is so easily and dramatically  increased.

So v2 > v1 and times t1 and t2 are both increased, so both areas A1 and A2 are increased.

The purple shaded areas indicate the increase in thinking distance A1 and braking distance A2.

This might mean lack of care and attention e.g. tired and not concentrating on the speed limit.

Rectangular area A1 = initial velocity v2 x reaction time t1 = thinking distance

Right angled triangular area A2 = ˝  x initial velocity v2 x braking time t2 = braking distance

So, both area A1 and A2 are greatly increased, increasing the likelihood of an accident if driving carelessly!

The total area = A1 + A2 = stopping distance, and much greater than before.

 

 If you have followed the above logical arguments, you should be able to interpret the graphs if only one factors was changed.

 

INDEX of physics notes on reaction times, stopping distances of road vehicles, Newton's 2nd Law, braking friction force, KE calculations

Key points force and motion: Road safety -

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations

Velocity–time graphs are a brilliant way to visualise thinking distance, braking distance, and stopping distance during an emergency stop. Here's how to interpret them:

Understanding the Graph

Thinking Distance

  • Graph section: Horizontal line (constant velocity)
  • Interpretation: The driver hasn’t applied the brakes yet but is reacting.
  • Distance: Area under the horizontal section

Braking Distance

  • Graph section: Sloping line down to zero velocity
  • Interpretation: Brakes are applied, and the vehicle decelerates.
  • Distance: Area under the triangle

Stopping Distance

  • Total area under the graph

Keywords, phrases and learning objectives for the physics of road vehicles - calculating stopping distances from graph

Be able to translate velocity-time graphs in terms of distances travelled.

How to calculate thinking distances and braking distances from velocity - time graphs for road vehicles

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INDEX of physics notes on reaction times, stopping distances of road vehicles, Newton's 2nd Law, braking friction force, KE calculations

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