{"id":119,"date":"2026-06-23T18:24:12","date_gmt":"2026-06-23T18:24:12","guid":{"rendered":"https:\/\/flowxiom.com\/?p=119"},"modified":"2026-06-23T18:48:51","modified_gmt":"2026-06-23T18:48:51","slug":"a-level-ial-unit-1-05-graphs-of-motion","status":"publish","type":"post","link":"https:\/\/flowxiom.com\/?p=119","title":{"rendered":"A- Level IAL Unit 1 05 Graphs of Motion"},"content":{"rendered":"\n

Unit 1 05 Graphs of Motion<\/h2>
<\/div><\/div>
<\/div>

1. Learning Objectives<\/h3><\/div>
    \n
  • <\/span>Subject Content:<\/strong>\n
      \n
    • <\/span>Interpret Displacement-time (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>) graphs<\/strong>: Gradient = Velocity.
      \n<\/li>\n
    • <\/span>Interpret Velocity-time (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>) graphs<\/strong>: Gradient = Acceleration; Area = Displacement.
      \n<\/li>\n
    • <\/span>Interpret Acceleration-time (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>) graphs<\/strong>: Area = Change in velocity.
      \n<\/li>\n
    • <\/span>Translate between different types of graphs (e.g., sketch <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> from <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>).
      \n<\/li>\n<\/ul>\n<\/li>\n
    • <\/span>Language Goals:<\/strong>\n
        \n
      • <\/span>Use descriptive verbs: “Accelerating”, “Decelerating”, “Stationary”, “Constant velocity”.
        \n<\/li>\n
      • <\/span>Explain the physical meaning of “Gradient” and “Area under the graph”.
        \n<\/li>\n<\/ul>\n<\/li>\n<\/ul><\/div>

        2. Key Terminology<\/h3><\/div>
        \n\n\n\n\n\n\n\n\n\n\n
        Term<\/strong><\/th>\nPhysical Meaning<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        Displacement-time graph<\/strong><\/td>\nShows position change.<\/td>\n<\/tr>\n
        Velocity-time graph<\/strong><\/td>\nShows speed\/direction change.<\/td>\n<\/tr>\n
        Gradient \/ Slope<\/strong><\/td>\nRate of change (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>).<\/td>\n<\/tr>\n
        Intercept<\/strong><\/td>\nInitial value (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>).<\/td>\n<\/tr>\n
        Area under the graph<\/strong><\/td>\nProduct of axes (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>).<\/td>\n<\/tr>\n
        Stationary \/ At rest<\/strong><\/td>\nVelocity = 0.<\/td>\n<\/tr>\n
        Uniform \/ Constant<\/strong><\/td>\nValue does not change.<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>
        <\/div>

        3. Displacement-Time Graphs (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/h3><\/div>

        The <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph tells us where<\/strong> an object is at any given time.<\/p><\/div>

        Key Rule:<\/strong><\/p><\/div>

        \n

        The Gradient of an <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph = Velocity (<\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/strong><\/p>\n<\/blockquote><\/div>

          \n
        • <\/span>Horizontal line:<\/strong> Gradient is 0 <\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> Velocity is 0 (Object is Stationary<\/strong>).
          \n<\/li>\n
        • <\/span>Straight diagonal line:<\/strong> Gradient is constant <\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> Velocity is constant (Uniform Velocity<\/strong>).
          \n<\/li>\n
        • <\/span>Curved line:<\/strong> Gradient is changing <\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> Velocity is changing (Accelerating<\/strong>).\n
            \n
          • <\/span>Curve getting steeper: Accelerating.
            \n<\/li>\n
          • <\/span>Curve getting flatter: Decelerating.
            \n<\/li>\n<\/ul>\n<\/li>\n<\/ul><\/div>

            \"Pasted<\/span><\/p><\/div>

            \n

            Tip:<\/strong> If the gradient is negative (sloping down), the object is moving backwards<\/strong> (returning to start).<\/p>\n<\/blockquote><\/div>

            <\/div>

            4. Velocity-Time Graphs (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/h3><\/div>

            The <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph is the most useful graph in A-level Physics because it links displacement and acceleration.<\/p><\/div>

            Key Rules:<\/strong><\/p><\/div>

              \n
            1. \n

              The Gradient = Acceleration (<\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/strong><\/p>\n

                \n
              • <\/span>Steep slope = High acceleration.
                \n<\/li>\n
              • <\/span>Horizontal line = Zero acceleration (Constant Velocity).
                \n<\/li>\n<\/ul>\n<\/li>\n
              • \n

                The Area under the graph = Displacement (<\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/strong><\/p>\n

                  \n
                • <\/span>Area above the t-axis is positive displacement (moving forward).
                  \n<\/li>\n
                • <\/span>Area below the t-axis is negative displacement (moving backward).
                  \n<\/li>\n<\/ul>\n<\/li>\n<\/ol><\/div>

                  \"Pasted<\/span><\/p><\/div>

                  \n

                  Exam Warning:<\/strong> Always check if the y-axis is Velocity<\/strong> or Speed<\/strong>.<\/p>\n

                    \n
                  • <\/span>Velocity-time<\/strong> graphs can go below the x-axis (negative direction).
                    \n<\/li>\n
                  • <\/span>Speed-time<\/strong> graphs can never be negative.
                    \n<\/li>\n<\/ul>\n<\/blockquote><\/div>
                    <\/div>

                    5. Acceleration-Time Graphs (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/h3><\/div>

                    These are generally simpler in Unit 2 (usually horizontal lines for constant acceleration).<\/p><\/div>

                    Key Rules:<\/strong><\/p><\/div>

                      \n
                    1. Horizontal line:<\/strong> Constant Acceleration.<\/li>\n
                    2. Area under the graph = Change in Velocity (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>)<\/strong><\/li>\n<\/ol><\/div>

                      \"Pasted<\/span><\/h4><\/div>

                      6. The “Golden Cycle” of Motion Graphs<\/h3><\/div>

                      To help students remember, we can summarize the chain of relationships between derivatives and integrals:<\/p><\/div>

                      <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-mspace><\/mjx-rbox><\/mjx-block><\/mjx-mpadded><\/mjx-over><\/mjx-c><\/mjx-ext><\/mjx-c><\/mjx-end><\/mjx-stretchy-h><\/mjx-mo><\/mjx-mstyle><\/mjx-base><\/mjx-mover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-mspace><\/mjx-rbox><\/mjx-block><\/mjx-mpadded><\/mjx-over><\/mjx-c><\/mjx-ext><\/mjx-c><\/mjx-end><\/mjx-stretchy-h><\/mjx-mo><\/mjx-mstyle><\/mjx-base><\/mjx-mover><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

                      <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-mspace><\/mjx-rbox><\/mjx-block><\/mjx-mpadded><\/mjx-over><\/mjx-c><\/mjx-ext><\/mjx-c><\/mjx-end><\/mjx-stretchy-h><\/mjx-mo><\/mjx-mstyle><\/mjx-base><\/mjx-mover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-mspace><\/mjx-mstyle><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-mspace><\/mjx-mstyle><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-c><\/mjx-mtext><\/mjx-mspace><\/mjx-rbox><\/mjx-block><\/mjx-mpadded><\/mjx-over><\/mjx-c><\/mjx-ext><\/mjx-c><\/mjx-end><\/mjx-stretchy-h><\/mjx-mo><\/mjx-mstyle><\/mjx-base><\/mjx-mover><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span><\/p><\/div>

                        \n
                      • <\/span>Moving forward (Derivation): Look at the Gradient<\/strong>
                        \n<\/li>\n
                      • <\/span>Moving backwards (Integration): Look at the Area<\/strong>
                        \n<\/li>\n<\/ul><\/div>
                        <\/div>

                        7. Practice Exercises<\/h3><\/div>

                        Q1.<\/strong> The displacement-time graph of an object is a straight line passing through the origin with a positive gradient. This indicates the object is:<\/p><\/div>

                        A. Stationary<\/p><\/div>

                        B. Moving with constant velocity<\/p><\/div>

                        C. Moving with constant acceleration<\/p><\/div>

                        D. Moving with increasing acceleration<\/p><\/div>

                        Q2.<\/strong> An object starts from rest and accelerates at <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span> for <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>, then travels at constant velocity for <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>.<\/p><\/div>

                          \n
                        • <\/span>(a) Sketch the velocity-time graph<\/strong> for this motion.
                          \n<\/li>\n
                        • <\/span>(b) Calculate the total displacement<\/strong> using the area method.
                          \n<\/li>\n<\/ul><\/div>

                          Q3.<\/strong> [Graph Interpretation] The velocity-time graph of a car shows it moving at <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>, then the line slopes down, crossing the time axis, and ends at <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>.<\/p><\/div>

                            \n
                          • <\/span>What is the physical meaning of the point where the line crosses the time axis (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>)?
                            \n<\/li>\n<\/ul><\/div>

                            \"Pasted<\/span>
                            \nQ4.<\/strong> A ball is dropped from a height and bounces back. Which of the following <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graphs best represents its motion (taking downward as positive)?<\/p><\/div>

                            (Use your imagination for the options, focus on the logic: Positive velocity <\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> sudden change to Negative velocity upon impact).<\/p><\/div>

                            <\/div>

                            Answers<\/h3><\/div>

                            Q1. Interpreting an <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph<\/h4><\/div>
                              \n
                            • <\/span>Analysis:<\/strong>\n
                                \n
                              • <\/span>The question describes a straight line<\/strong> displacement-time (<\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>) graph passing through the origin, and the gradient is positive.
                                \n<\/li>\n
                              • <\/span>According to the rule: The Gradient of an <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph = Velocity<\/strong>.
                                \n<\/li>\n
                              • <\/span>Since it is a straight line, it means the gradient is constant.
                                \n<\/li>\n
                              • <\/span>Since the gradient is positive, it means the velocity is positive.
                                \n<\/li>\n
                              • <\/span>Therefore, the object is moving with a constant positive velocity.
                                \n<\/li>\n<\/ul>\n<\/li>\n
                              • <\/span>Correct Answer: B. Moving with constant velocity<\/strong>
                                \n<\/li>\n<\/ul><\/div>
                                <\/div>

                                Q2. Sketching and Calculating from a v-t graph<\/h4><\/div>

                                Description:<\/strong> Starts from rest, accelerates at <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-texatom><\/mjx-script><\/mjx-msup><\/mjx-math><\/mjx-container><\/span> for <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>, then travels at constant velocity for <\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>.<\/p><\/div>

                                (a) Sketch the velocity-time graph:<\/strong><\/p><\/div>

                                  \n
                                1. \n

                                  Stage 1 (0-5s): Uniform acceleration.<\/strong><\/p>\n

                                    \n
                                  • <\/span>Starting point: <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span> (starts from rest).
                                    \n<\/li>\n
                                  • <\/span>Because acceleration is the gradient of the <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span> graph, this is a straight line starting from the origin with a gradient of <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>.
                                    \n<\/li>\n
                                  • <\/span>At <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>, the velocity <\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>.
                                    \n<\/li>\n
                                  • <\/span>Drawing: A straight line connecting the point <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> to the point <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span>.
                                    \n<\/li>\n<\/ul>\n<\/li>\n
                                  • \n

                                    Stage 2 (5-10s): Uniform velocity.<\/strong><\/p>\n

                                      \n
                                    • <\/span>The velocity remains constant at <\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mtext><\/mjx-c><\/mjx-mi><\/mjx-c><\/mjx-mo><\/mjx-texatom><\/mjx-c><\/mjx-mi><\/mjx-math><\/mjx-container><\/span>.
                                      \n<\/li>\n
                                    • <\/span>The acceleration is <\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span> (gradient is <\/mjx-c><\/mjx-mn><\/mjx-math><\/mjx-container><\/span>).
                                      \n<\/li>\n
                                    • <\/span>Drawing: A horizontal straight line from the point <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span> to the point <\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-c><\/mjx-c><\/mjx-mn><\/mjx-c><\/mjx-mo><\/mjx-math><\/mjx-container><\/span>.
                                      \n<\/li>\n<\/ul>\n<\/li>\n<\/ol><\/div>

                                      (b) Calculate the total displacement:<\/strong><\/p><\/div>