Distance-time graphs and contextual intersections · Higher
| English | 中文 | Pinyin |
|---|---|---|
| stationary/ˈsteɪʃənəri/ | 静止的 | jìng zhǐ de |
Where is the waiting time on the graph?
- A delivery rider travels, waits, then travels again. Which parts of a distance-time graph reveal the waiting time?
- This lesson studies stationary 静止的: Not changing position over the time interval described.
Choose the mathematical structure
- Read the axis quantities and units before interpreting shape. On a distance-time graph, slope is speed for a segment with increasing distance; a horizontal segment means no distance change. An intersection of two charge graphs gives equal costs. A curved section requires a local rather than one fixed slope.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines stationary?
Not changing position over the time interval described.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
The distance points (0,0),(2,6),(5,6),(7,10), in seconds and metres, give speed 6/2=3 m/s for the first section, a 3-second stop, then speed (10-6)/(7-5)=2 m/s. Average speed for the full interval is 10/7 m/s, including the stop. Charges 20+3x and 44+x meet at x=12, at cost 56. If speed increases from 0 to 10 m/s over 5 seconds, its average acceleration is 10/5=2 m/s²; a speed-time graph measures this through its slope.
Distance-time graphs and contextual intersections
Read the axis quantities and units before interpreting shape
Compare the model with the worked case and explain one change.
Find the first-segment speed.
Change of distance 6 divided by elapsed time 2.
Test a tempting shortcut
- A horizontal distance graph does not mean fast motion. A graph height gives distance, while slope gives its rate. Average speed includes every elapsed interval, including waiting.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A horizontal segment on a distance-time graph means the object is moving at its greatest speed. This claim is false. Explain which definition or assumption it violates.
Find the duration of the stop.
The horizontal section runs from minute 2 to minute 5.
A horizontal segment on a distance-time graph means the object is moving at its greatest speed.
A horizontal distance graph does not mean fast motion. A graph height gives distance, while slope gives its rate. Average speed includes every elapsed interval, including waiting.
Interpret a new situation
- AQA A14 uses real contexts and graphical solutions. Foundation can interpret a plotted non-standard function; Higher also interprets exponential models and nonlinear graph estimates in the next lesson.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the final-segment speed.
(10-6)/(7-5)=2.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.2. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
Not changing position over the time interval described. Choose the relationship, show the method, check its assumptions and interpret the result.