Level 3 Integration Walkthrough
2020 NCEA Level 3 Integration Question 1(b)
2020 Paper
Question
For \(t\ge0\), the velocity of an object is given by \(v(t)=0.6\sqrt{t}\), where \(v\) is the velocity of the object in centimetres per second and \(t\) is time in seconds from the start of the object's motion.
The object has a displacement of \(5\) centimetres at \(t=0\). What will be the displacement of the object after \(16\) seconds?
First walkthrough idea
Focus to try first
Velocity is the derivative of displacement, so integrate \(v(t)\), use \(s(0)=5\), then evaluate \(s(16)\).
Step 1
Integrate the velocity
Rewrite the square root in exponential form before applying the power rule.
Show the first step’s working
Walkthrough overview
What this question practises
This 2020 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Integrating velocity and using the initial displacement.
This is Question 1(b) from the 2020 NCEA Level 3 Integration paper for AS91579 — Apply integration methods in solving problems. Use the guided hints to practise the method before revealing the full working.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91579.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise integrating velocity and using the initial displacement. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check the antiderivative by differentiating it, and handle constants and bounds explicitly.
Continue practising
- All 2020 Integration walkthroughs
- All AS91579 Integration years
- Practise more questions using this skill: Antidifferentiation