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ASPhysicsCIERevision Notes2. Kinematics2.1 Equations of MotionArea under a Velocity-Time Graph

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

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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 Tip

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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    Ashika

    Author: Ashika

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    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.