M14 Graphs in context mind map

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M14 Graphs in context mind map

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Context

Read axes: Identify quantity, scale and units; model has a valid range
Intersection: Taxi models meet at d=6 km, C=£16
Fixed journey: Time = distance/speed; reciprocal if distance fixed

Movement

Distance–time: Gradient = speed; horizontal = stationary
Displacement: Gradient = signed velocity; cumulative distance never falls
Velocity–time: Horizontal = constant velocity; negative = opposite direction

Area / acceleration

Gradient: Higher: Velocity–time gradient = acceleration in m/s²
Area: Higher: Signed area = displacement; magnitudes total distance
Approximation: Higher: Rectangles/trapezia estimate curved areas; smaller strips help

Curved rates

Tangent / chord: Higher: Tangent: instantaneous; chord: average rate
Interpret units: Higher: Gradient and area meanings depend on axes

Connections

Context → Movement: Axis quantities determine gradient meaning
Movement → Curved rates: Curved graphs distinguish average and instant rates