Real-context graphs and kinematics
OCR J560 graphs show distance, speed, water depth, mobile-phone tariffs, and other applied contexts. Reading the gradient and area gives quantitative answers; describing what each section means gives qualitative ones.
Distance–time graphs
Axes: time t (horizontal), distance d (vertical).
- Gradient = speed. Steeper line → faster.
- Horizontal line → stationary (speed 0).
- Curved line → changing speed (acceleration or deceleration).
- Negative gradient → moving back toward start.
Speed–time (velocity–time) graphs
Axes: time t (horizontal), speed v (vertical).
- Gradient = acceleration.
- Area under graph = distance travelled.
- Horizontal line → constant speed.
- Triangular section: distance = ½ × base × height.
- Trapezoidal section: distance = ½ × (a + b) × h.
Water depth / filling graphs
A container being filled at a constant rate produces a depth–time graph whose shape reveals the cross-section of the container:
- Cylinder: straight line (constant rate).
- Cone (point down): curves slowly at first, then rapidly.
- Wide-then-narrow: shallow then steep.
✦Worked example— Worked example — speed–time
A car accelerates uniformly from rest to 20 m/s in 5 s, holds 20 m/s for 10 s, decelerates uniformly to rest in 5 s. Find total distance.
Triangle 1: ½ × 5 × 20 = 50 m. Rectangle: 10 × 20 = 200 m. Triangle 2: ½ × 5 × 20 = 50 m. Total: 300 m.
Average speed = 300 / 20 = 15 m/s.
OCR mark scheme conventions
- M1 for splitting the area into trapezia/triangles/rectangles.
- A1 for each correctly-evaluated piece.
- A1 for the total distance.
- "Describe the journey" requires units and direction (e.g. "stationary for 10 s, then travels at 5 m/s away from start").
⚠Common mistakes
- Confusing distance–time with speed–time graphs.
- Reading the y-value as distance on a speed–time graph.
- Forgetting that area = distance on speed–time, not the gradient.
- Wrong units — m/s vs km/h needs explicit conversion.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves