When force depends on position or velocity, acceleration is no longer constant and calculus is required. Choosing the right form of acceleration is the whole battle.
Syllabus points covered
- Use Newton's second law with acceleration expressed as dv/dt or v dv/dx
- Solve problems where the force depends on time, displacement or velocity
- Set up and solve the resulting differential equation
- Interpret the solution, including terminal velocity
Common mistakes
- Using dv/dt when the force depends on displacement, where v dv/dx is the useful form.
- Losing the constant of integration and with it the initial condition.
- Separating variables incorrectly and leaving mixed terms on one side.
- Forgetting that terminal velocity occurs where acceleration, not velocity, is zero.
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 questions
- Mark scheme
- Step-by-step worked solutionsComing soon
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