Graphs in practical situations · ⁨实际情境中的图⁩

Reading the story in a graph

• A distance–time graph is not just a line — it's a story of a journey. A steep section means fast travel; a flat section means stopped.
• Every graph tells a story through its shape and gradient 斜率.

Distance–time graphs

• Gradient = speed (distance ÷ time).
• Steeper line = faster speed.
• Flat line = stationary (not moving).
• Curved line = changing speed (accelerating or decelerating).

On a distance-time graph the gradient is the speed; a flat section means the object has stopped

Speed–time graphs (Extended)

• Gradient = acceleration 加速度 (change in speed ÷ time).
• Area under the graph = total distance travelled.

The area under a speed–time graph gives the distance: triangle $+$ rectangle $= 80 + 240 = 320$ m.

Worked example

• A car accelerates from rest to 20 m/s in 8 s, then travels at 20 m/s for 12 s.
• Acceleration $= \dfrac{20}{8} = 2.5$ m/s² (the gradient of the first section).
• Distance $= \dfrac{1}{2}(8)(20) + (12)(20) = 80 + 240 = 320$ m (area of triangle + rectangle).

On a speed-time graph the gradient is the acceleration and the area underneath is the distance travelled

Conversion graphs 换算图

• A conversion graph is a straight line that converts between two units.
• Miles to km: draw a line through $(0, 0)$ and $(5, 8)$ (5 miles ≈ 8 km).
• Read across from one axis, up/down to the line, then across to the other axis.

You've got it