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CIE AS Maths: Mechanics

Revision Notes

Home / AS / Maths: Mechanics / CIE / Revision Notes / 2. Kinematics (Straight Line Motion) / 2.1 Kinematics Graphs / 2.1.1 Displacement-Time Graphs


2.1.1 Displacement-Time Graphs


Displacement-Time Graphs

What is a displacement-time graph?

  • Displacement-time graphs show the displacement of an object from a fixed origin as it moves in a straight line
  • They show displacement (on the vertical axis) against time (on the horizontal axis)
  • Displacement-time graphs can go below the horizontal axis whereas distance-time graphs can not
    • Distance can not be negative whereas displacement can be

What are the key features of a displacement-time graph?

  • The gradient of the graph equals the velocity of the object
    • A positive gradient means the object is travelling forwards
    • A negative gradient means that the object is travelling backwards
    • The steeper the line, the greater the speed

  • A straight line shows that the object is moving at a constant velocity
  • A curved line shows that the object is accelerating or decelerating
  • A horizontal line shows that the object is stationary
  • If the graph touches the x-axis, then the object is at the origin at that time

2-1-1-displacement-time-graphs-diagram-1

How do I find the average speed and the average velocity of a journey?

Average space speed =  fraction numerator Total space distance space travelled over denominator Time space taken end fraction

  • The average speed can not be negative as speed is a scalar quantity and can only take a positive value

Average space velocity space equals space fraction numerator Displacement space from space starting space point over denominator Time space taken end fraction

  • The average velocity is a vector quantity and can be positive, zero or negative

Worked Example

(a)   Calculate the velocity of the athlete during the first 2 seconds.

2-1-1-displacement-time-graphs-example-solution-1-a

(b)    Describe the motion of the athlete between the times of 2 seconds and 5 seconds.

2-1-1-displacement-time-graphs-example-solution-1-b

(c)   Calculate the velocity of the athlete at 10 seconds.

2-1-1-displacement-time-graphs-example-solution-c

(d)   Find the total distanced travelled by the athlete during the 14 seconds.

2-1-1-displacement-time-graphs-example-solution-d

Exam Tip

  • Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.
  • Be careful to spot if you are working with a displacement-time graph or a distance-time graph
  • Check where the graph starts from on the y-axis, the object does not have to start at 0. For example, if the graph starts at 100, the scenario could be a student on a walk starting 100 m from their house.
  • Distance is a scalar so it can not be negative whereas displacement from a starting point can be.
  • Think about the units when calculating, make sure they are consistent.


  • 1. Mechanics Toolkit
    • 1.1 Quantities, Units & Modelling
      • 1.1.1 Scalars & Vectors
        • 1.1.2 Fundamental Units
          • 1.1.3 Derived Units
            • 1.1.4 Types of Force
              • 1.1.5 Modelling Assumptions
            • 2. Kinematics (Straight Line Motion)
              • 2.1 Kinematics Graphs
                • 2.1.1 Displacement-Time Graphs
                  • 2.1.2 Velocity-Time Graphs
                    • 2.1.3 Drawing Travel Graphs
                    • 2.2 Variable Acceleration
                      • 2.2.1 Using Calculus in 1D
                      • 2.3 Constant Acceleration
                        • 2.3.1 Deriving the suvat Formulae
                          • 2.3.2 suvat in 1D
                            • 2.3.3 Acceleration due to Gravity
                          • 3. Forces & Newton’s Laws
                            • 3.1 Forces
                              • 3.1.1 Force Diagrams
                                • 3.1.2 Equilibrium in 1D
                                  • 3.1.3 Equilibrium in 2D
                                  • 3.2 Newton's Second Law
                                    • 3.2.1 F = ma
                                      • 3.2.2 Connected Bodies - Ropes & Tow Bars
                                        • 3.2.3 Connected Bodies - The Lift Problem
                                          • 3.2.4 Connected Bodies - Pulleys
                                          • 3.3 Further Forces & Newton's Laws
                                            • 3.3.1 Resolving Forces & Inclined Planes
                                              • 3.3.2 Coefficient of Friction
                                                • 3.3.3 Coefficient of Friction - F = ma
                                                  • 3.3.4 Coefficient of Friction - Inclined Planes
                                                    • 3.3.5 Coefficient of Friction - Harder Problems
                                                  • 4. Energy, Work & Power
                                                    • 4.1 Work & Energy
                                                      • 4.1.1 Work
                                                        • 4.1.2 Energy
                                                          • 4.1.3 Energy Principles
                                                          • 4.2 Power
                                                            • 4.2.1 Power
                                                          • 5. Momentum
                                                            • 5.1 Momentum & Collisions
                                                              • 5.1.1 Momentum
                                                                • 5.1.2 Direct Collisions
                                                                  • 5.1.3 Collisions - Multiple Collisions


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                                                                Author: Daniel

                                                                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.


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