LuduminaFM-08 · FM-U3 · Planned
Distance–time graphs
Learning objectives
Translate motion into a distance–time graph; calculate straight-line gradients; H: estimate instantaneous speed using a tangent.
8463 §§4.5.6.1.4 / 8464 §§6.5.4.1.4
DfE single-science pp.35–37 / Combined pp.30–32. Evidence checked 30 September–1 October 2026. Skills: WS3.1,3.2; MS4a–4e.
Needs firstFM-07
Explanation
A distance–time gradient gives speed. A horizontal segment means no additional distance is travelled. A tangent estimates the instantaneous speed on a curved trace; that tangent skill is Higher-only here.
Concepts, equations and units: Gradient=Δdistance/Δtime in m/s; axes m and s; tangent only H.
Prediction, demonstration and game exercise
Predict, observe, explain
Predict graph segments for rest and changing speed; replay position data against the graph.
Planned learner game exercise
Drive a cart to match three graph segments; H: place a tangent on a curve.
Independent practice
Plot measurements, find two gradients and explain a horizontal section.
Original practice example · Shared
A straight distance–time segment goes from 4 s, 8 m to 10 s, 26 m. Find speed.
Show working and model answer
Working / reasoning
Gradient = (26 − 8)/(10 − 4) = 18/6.
Answer
3 m/s.
Exit check and success criteria
Labelled graph and two correct gradients; H tangent uses a sensible large triangle.
During practice, compare the prediction with evidence and give an error-specific prompt. The exit item uses a fresh context or fresh values, answered independently.
Misconceptions, practical links and mastery
Check these misconceptions
Graph depicts the physical hill; steeper means greater acceleration on every graph; distance graph decreases on return.
Practical preparation
Optional motion measurements, AT1,3.
Virtual preparation and revision only. Required hands-on activities and school records remain separate.
Proposed mastery
0: not yet evidenced. 1: supported. 2: independent exit criteria met. 3: successful changed-context transfer. Advance at 2; revisit with fresh retrieval. These are not GCSE grades.