Motion described by calculus. Displacement, velocity and acceleration are linked by differentiation one way and integration the other, and the whole topic is knowing which direction you're travelling in.
Syllabus points covered
- Apply differentiation and integration to displacement, velocity and acceleration
- Use the relationships v = ds/dt and a = dv/dt
- Find displacement from velocity and velocity from acceleration by integration
- Solve problems involving maximum displacement, instantaneous rest and distance travelled
Common mistakes
- Confusing distance travelled with displacement when the object changes direction. Find when v = 0 and split the journey.
- Differentiating when you should integrate. Going from displacement to velocity differentiates; the reverse integrates.
- Forgetting the constant of integration and losing the initial condition the question gave you.
- Assuming the particle is at rest when acceleration is zero — that's when velocity is at a maximum or minimum.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
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