Area under a Velocity-Time Graph (Edexcel IGCSE Physics (Modular))

Revision Note

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Ashika

Written by: Ashika

Reviewed by: Caroline Carroll

Area under a velocity-time graph

How to find the area under a velocity-time graph

  • The area under a velocity-time graph represents the displacement (or distance travelled) by an object

Velocity-Time Area graph, downloadable IGCSE & GCSE Physics revision notes

The displacement, or distance travelled, is represented by the area beneath the graph

 

  • If the area beneath the velocity-time graph forms a triangle (i.e. the object is accelerating or decelerating), then the area can be determined by using the following formula:

Area = ½ × Base × Height

  • If the area beneath the velocity-time graph forms a rectangle (i.e. the object is moving at a constant velocity), then the area can be determined by using the following formula:

Area = Base × Height

How to find distance from a velocity-time graph

  • Enclosed areas under velocity-time graphs represent total displacement (or total distance travelled) in a time interval

Determining Distance on a V-T graph, downloadable IGCSE & GCSE Physics revision notes

Three enclosed areas (two triangles and one rectangle) under this velocity-time graph represent the total distance travelled in the total time

  • If an object moves with constant acceleration, its velocity-time graph will consist of straight lines

    • In this case, calculate the distance travelled by working out the area of enclosed rectangles and triangles

    • The area of each enclosed section represents the distance travelled in that particular interval of time

    • The total distance travelled is the sum of all the individual enclosed areas

Worked Example

The velocity-time graph below shows a car journey that lasts for 160 seconds.

Area Under a V-T graph question, downloadable IGCSE & GCSE Physics revision notes

Calculate the total distance travelled by the car.

Answer:

Step 1: Recall that the area under a velocity-time graph represents the distance travelled

  • In order to calculate the total distance travelled, the total area underneath the line must be determined

Step 2: Identify each enclosed area

  • In this example, there are five enclosed areas under the line

  • These can be labelled as areas 1, 2, 3, 4 and 5, as shown in the image below:

Area Under a V-T graph solution, downloadable IGCSE & GCSE Physics revision notes

Step 3: Calculate the area of each enclosed shape under the line

  • Area 1 = area of a triangle

A subscript 1 space equals space 1 half space cross times space base space cross times space height

A subscript 1 space equals space 1 half space cross times space 40 space cross times space 17.5

A subscript 1 space equals space 350 space straight m

  • Area 2 = area of a rectangle

A subscript 2 space equals space base space cross times space height

A subscript 2 space equals space 30 space cross times space 17.5

A subscript 2 space equals space 525 space straight m

  • Area 3 = area of a triangle

A subscript 3 space equals space 1 half space cross times space base space cross times space height

A subscript 3 space equals space 1 half space cross times space 20 space cross times space 7.5

A subscript 3 space equals space 75 space straight m

  • Area 4 = area of a rectangle

A subscript 4 space equals space base space cross times space height

A subscript 4 space equals space 20 space cross times space 17.5

A subscript 4 space equals space 350 space straight m

  • Area 5 = area of a triangle

A subscript 5 space equals space 1 half space cross times space base space cross times space height

A subscript 5 space equals space 1 half space cross times space 70 space cross times space 25

A subscript 5 space equals space 875 space straight m

Step 4: Calculate the total distance travelled by finding the total area under the line

  • Add up each of the five areas enclosed:

total space distance space equals space A subscript 1 space plus space A subscript 2 space plus space A subscript 3 space plus space A subscript 4 space plus space A subscript 5

total space distance space equals space 350 space plus space 525 space plus space 75 space plus space 350 space plus space 875

total space distance space equals space 2175 space straight m

Examiner Tips and Tricks

Some areas will need to be split into a triangle and a rectangle to determine the area for a specific time interval, like areas 3 & 4 in the worked example above.

If you are asked to find the distance travelled for a specific time interval, then you just need to find the area of the section above that time interval.

For example, the distance travelled between 70 s and 90 s is the sum of Area 3 + Area 4

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.

Caroline Carroll

Author: Caroline Carroll

Expertise: Physics Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.