Calculus
Understanding Motion worksheets
Analyze polynomial position for velocity, direction changes, direction intervals, and displacement.
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Related Rates worksheets
Differentiate geometric constraints with respect to time and solve unit-aware instantaneous rates.
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Write the constraint, differentiate with respect to time, then substitute the instant and report signed units.
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Each worked key keeps the defining constraint, derivative reasoning, exact result, and contextual units together.
Learning objective
What this activity builds
Relate changing quantities, differentiate before substitution, and preserve the sign and units of the requested rate.
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When should numbers be substituted?
After differentiating with respect to time.
Substituting a changing quantity too early incorrectly treats it as constant.
Teaching notes
Make the practice count
- Mark fixed and changing quantities.
- Attach a time derivative to every changing variable.
- Interpret a negative answer as decreasing.
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