Lesson 5: Speed-Time Graphs, Acceleration & Distance Calculation
Exploring forces, net force calculations, motion graphs, energy, and real-world NZ physics applications.
🎯 Ngā Whāinga Akoranga | Learning Intentions
How speed-time (v-t) graphs represent motion: flat line = constant speed, slope = acceleration (a = Δv / Δt in m/s²), and area under the graph = total distance travelled.
Calculate acceleration from v-t graph gradients, calculate total distance by finding the area of geometric shapes (rectangles and triangles) under the line.
🎥 Media Anchor & Pedagogical Scaffold
Speed-Time Graphs: Acceleration & Area Distance
Video Clip: Velocity-time graphs — calculating acceleration from gradient and distance from area (Runtime: 6m 45s).
🧠 1. Before Viewing (Activate & Predict)
How can you calculate the total distance travelled by a accelerating car using just its speed-time graph?
👁️ 2. During Viewing (Watch With a Job)
- Formula: from a speed-time graph, how do you calculate acceleration? (hint: what does the gradient represent?)
- Area: a speed-time graph shows a trapezoid. Explain how the area under the graph gives you distance — not speed.
- Compare: how is a speed-time graph different from a distance-time graph in what it tells you about motion?
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Model breaking complex speed-time graphs into colour-coded triangles and rectangles on graph paper.
Immediate Task: Complete Worksheet 5: Speed-Time Graph Acceleration & Area Under Curve Problem Set.
⚡ Whakaoho | Do Now: Same Flat Line, Different Meaning
On a distance-time graph, a flat line means stopped. Two minutes: what does a flat line mean on a speed-time graph?
Write your answer before checking. This one confusion costs more marks in this topic than anything else, and once you have seen it clearly it stops costing you anything.
📖 Activity 1: Gradient Gives Acceleration, Area Gives Distance
Find the acceleration (13 min). For each sloped section calculate a = Δv / Δt, units m/s². A section sloping downward gives a negative answer, and that is correct — it means slowing down. Do not drop the minus sign to make it look tidier.
Find the distance (12 min). Split the area under the line into rectangles and triangles, calculate each, add them. Then check the units: m/s multiplied by s gives m. If your units do not come out as metres, something went wrong in the method, not the arithmetic.
📝 Activity 2: Year 10 Physics Worksheet & Explanation Scaffolding (20 mins)
Logbook Section 5. Record: (1) acceleration for every section with working and units; (2) total distance from the area, showing the shapes you split it into; (3) one clear sentence on the difference between a flat line on a distance-time graph and a flat line on a speed-time graph.
🏫 Kaiako Planning & Pedagogy Notes
Year 10 Curriculum Alignment: NZ Curriculum Phase 4 Science — Physical World strand. Builds foundational physics problem-solving skills for NCEA Level 1 Mechanics and Level 2 Physics.