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ASPhysicsCambridge (CIE)Revision Notes2. KinematicsEquations of MotionArea under a Velocity-Time Graph

Area under a Velocity-Time Graph (Cambridge (CIE) AS Physics)

Revision Note

Ashika

Written by: Ashika

Reviewed by: Caroline Carroll

Updated on

Area under a velocity-time graph

  • Velocity-time graphs show the speed and direction of an object in motion over a specific period of time

  • The area under a velocity-time graph is equal to the displacement of a moving object

  • The area under a graph can be sectioned into triangles and rectangles to make the calculations easier

  • The area of a triangle can be found with the following formula:

A subscript t r i a n g l e end subscript space equals space 1 half b h

  • The area of a rectangle can be found with the following formula:

A subscript r e c t a n g l e end subscript space equals space b h

  • Where:

    • A = area

    • b = length of base

    • h = height

Worked Example

The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.

v-t Area Worked Example (1), downloadable AS & A Level Physics revision notes

Calculate the displacement of the vehicle at 40 s.

Answer:

Step 1: State how to determine the displacement

  • The displacement is equal to the area under a velocity-time graph

Step 2: Determine the scale on the graph

  • Each division is 50 over 10 space equals space 5 space km space straight h to the power of negative 1 end exponent

2-1-3-we-v-t-answer-cie-new

Step 3: Determine the base and height of the graph

  • Time = base = 40 s

  • Velocity = height = 105 km h–1

Step 4: Convert km h-1 into km s–1

fraction numerator 105 over denominator 60 space cross times space 60 end fraction space equals space 0.0292 space km space straight s to the power of negative 1 end exponent

Step 5: Calculate the area under the graph

 Area of a right-angled triangle =  1 half space cross times space b a s e space cross times h e i g h t

A r e a space equals 1 half space cross times space 40 space cross times space 0.0292 space equals space 0.6 space km space

Examiner Tips and Tricks

Always check the values given on the y-axis of a motion graph - students often confuse displacement-time graphs and velocity-time graphs.

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    Previous:Motion GraphsNext:Gradient of a Displacement-Time Graph
    Author
    Reviewer
    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.