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International A LevelMaths: Mechanics 1EdexcelRevision Notes2. Kinematics (Straight Line Motion)2.1 Kinematics Graphs2.1.3 Acceleration-Time Graphs

Acceleration-Time Graphs (Edexcel International A Level Maths: Mechanics 1): Revision Note

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Dan

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Acceleration-Time Graphs

What is an acceleration-time graph?

  • Acceleration-time graphs show the acceleration of an object as it moves in a straight line
  • They show acceleration (on the vertical axis) against time (on the horizontal axis)
  • Acceleration-time graphs can go below the horizontal axis

What are the key features of an acceleration-time graph?

  • A horizontal line shows that the object is accelerating at a constant rate
  • If the graph touches the x-axis then the object is moving with constant velocity at that time
  • If the graph is above the x-axis then the object has positive acceleration and its velocity is increasing which means
    • It is speeding up if it is moving forward
    • It is slowing down if it is moving backwards
  • If the graph is below the x-axis then the object has negative acceleration and its velocity is decreasing which means
    • It is slowing down if it is moving forward
    • It is speeding up if it is moving backwards
  • The area between graph and the x-axis tells us the change in velocity of the object
    • Graph above the x-axis means the velocity of the object is increasing
    • Graph below the x-axis means the velocity of the object is decreasing
  • The total change in velocity of the object from its starting point is the sum of the areas above the x-axis minus the sum of the areas below the x-axis2-1-3-acceleration-time-graphs-diagram-1

What does an acceleration-time graph NOT show?

  • You can not tell the velocity of the object at a specific time just by looking at an acceleration-time graph
    • You can calculate this using the areas between the graph and the x-axis if you know the initial velocity of the object
    • If the acceleration-time graph is positive this does not guarantee that the velocity will be positive

Worked example

2-1-3_we_acceleration-time-graph

(i)
the speed of the car after 2 seconds,
E_LDGidW_2-1-3-acceleration-time-graphs-example-solution_a
(ii)
the distance travelled between the times t equals 2 and t equals 6,
2-1-3-acceleration-time-graphs-example-solution_b-1
(iii)
the speed of the car after 8 seconds.
IOU1Baz~_2-1-3-acceleration-time-graphs-example-solution_c

Examiner Tip

  • Most of the time the acceleration-time graphs you will encounter will comprise of three disjointed horizontal lines, acceleration-time graphs will not have curved or diagonal lines for this course. Though in real life acceleration is likely to vary.

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    Dan

    Author: Dan

    Expertise: Maths

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.