Year 12 · Specialist Mathematics

Related rates, velocity and tangents

Free examples and worked answers. No account needed.

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Practise the method.

Connect changing quantities and vector motion.

Example 1

rGold: radius 7 cm at the given instant
Explore a later radius while radial speed stays 6 cm/s. The gold outline preserves the question instant; volume and its rate are not calculated.
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Answer:

Example 2

-1.216.8-1.622.4xy
Dots mark equal quarter-second intervals. Move the particle and compare horizontal and vertical displacement. Equal spatial scales; the displayed time window is 0–1 s.
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Answer:

Example 3

rGold: radius 4 cm at the given instant
Explore a later radius while radial speed stays 5 cm/s. The gold outline preserves the question instant; volume and its rate are not calculated.
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Answer: