Graphs in practical situations
Graphs in practical situations
- The gradient of a graph shows a rate of change.
- a distance–time graph: gradient = speed; a flat part means not moving.
- a conversion graph: a straight line to change between two units.
Practice
On a distance–time graph, the gradient represents the:
Distance ÷ time = speed, which is the gradient.
Speed–time graphs (Extended)
- gradient = acceleration; area under = distance travelled.
- Example: 0 → 20 m/s in 8 s, then 20 m/s for 12 s. Acceleration $= \tfrac{20}{8} = 2.5$ m/s²; distance $= \tfrac12(8)(20) + 12(20) = 320$ m.
Practice
A car speeds up from rest to 20 m/s in 8 s. What is the acceleration (m/s²)?
acceleration = 20/8 = 2.5 m/s² (the gradient of the speed–time graph).
Practice
Then it stays at 20 m/s for 12 s. Total distance = ½(8)(20) + 12(20). What is it (m)?
Area = triangle 80 + rectangle 240 = 320 m.
You've got it
Key idea
- distance–time gradient = speed; flat = stationary
- speed–time gradient = acceleration; area = distance
- a conversion graph changes between two units