Reading and Interpreting Graphs
Drag two handles along a real physics graph: a gradient triangle is drawn between them and the area beneath is shaded, both computed exactly and both labelled with what they physically mean on that particular graph. Four graphs — speed–time, distance–time, force–extension and voltage–current — chosen so the same two operations mean four different things: gradient is acceleration on one and spring constant on another. Two of them deliberately have no meaningful area, and the sim says so rather than quietly printing a number, because knowing when not to calculate the area is as important as knowing how. Spanning a corner in the line triggers a warning that the reading is an average gradient, not a value at a point. Gradients and areas verified against 19 hand-derived values, including intervals crossing breakpoints.
The richest graph on the syllabus: gradient gives acceleration, area gives distance. A negative gradient is deceleration — but the area is still a positive distance.
Faced with any graph, ask two things: what does the gradient represent? and what does the area represent?
The answer comes from the units. Divide the y-unit by the x-unit and you get the gradient's meaning; multiply them and you get the area's. m/s ÷ s = m/s², acceleration. m/s × s = m, a distance.
1. On the speed–time graph, put both handles inside the first slope and read the acceleration. Then drag one past the corner — the warning appears, because a single triangle can no longer describe two different slopes.
2. Shade the whole speed–time graph. The total area is the total distance travelled — including the deceleration, which still covers ground.
3. Switch to distance–time and shade the area. A number appears, but it means nothing. Getting an answer is not the same as getting a physical quantity.
Meanings To Know
Distance–time — gradient is speed
Speed–time — gradient is acceleration, area is distance
Force–extension — gradient is k, area is energy stored
Voltage–current — gradient is resistance