Real-context graphs and kinematics

WJEC routinely asks candidates to read, plot or interpret graphs that model real situations: distance–time, speed–time, conversion graphs and container-fill graphs.

Distance–time graphs

The vertical axis is distance from a starting point; the horizontal axis is time.

• Gradient = speed.
• Horizontal line = stationary (zero gradient).
• Steeper line = faster.
• Returning to the start: the line comes back down to zero.

A return journey shows a triangular outline; total distance is the SUM of the up and down legs (not the difference).

Speed–time graphs

Vertical axis is speed; horizontal axis is time.

• Gradient = acceleration (positive) or deceleration (negative).
• Area under the curve = distance travelled.
• Horizontal line = constant speed.

For a trapezium-shaped speed–time graph, distance = (1/2)(a + b)h where a and b are the parallel sides.

Conversion graphs

A straight line through the origin converts one unit to another (e.g. £ to €). Read off by dropping vertical/horizontal lines.

Container fill / depth–time graphs

The shape of the curve depends on the container's cross-section:

• Wide container fills slowly → shallow gradient.
• Narrow container fills quickly → steep gradient.
• A vase-shape (narrow bottom, wide middle, narrow top) gives a curve that is steep, then shallow, then steep again.

Kinematic word problems

Common WJEC patterns:

• "Estimate the speed at t = 5 s" → tangent to the curve at that point, then gradient.
• "Find the total distance travelled" → area under the speed–time graph.
• "When was the object stationary?" → where the distance–time graph is horizontal.

WJEC exam tip

When the graph is on a printed grid, draw faint horizontal/vertical guide lines BEFORE writing your answer — examiners credit method marks M1 for visible construction lines even if your final number is slightly off.