Level 2 Calculus Walkthrough
2025 NCEA Level 2 Calculus Question 1(d)
2025 Paper — Catch-up distance using displacement equations
Question
The Helena moves at \(5\text{ m s}^{-1}\) and is already \(200\text{ m}\) from the dock.
A smaller boat leaves the dock from rest and accelerates at \(0.5\text{ m s}^{-2}\).
Find the distance from the dock at which the smaller boat catches the Helena.
Find a displacement equation for each boat, set them equal, solve for the time, then substitute back to find the distance from the dock.
First walkthrough idea
Tip to try first
Use the Helena's 200 m head start when you write its displacement equation.
Step 1
Write the Helena's displacement equation
Reveal the explanation and working for this step.
Show the first step’s working
Let \(t\) be the number of seconds after the smaller boat leaves the dock, then write the Helena's displacement model.
Key result
The Helena is already 200 m from the dock when \(t=0\), and then it keeps moving at a constant 5 m/s.
Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91262 — Apply calculus methods in solving problems.
Method: Writing displacement equations, solving when they are equal, and answering in context.
This is Question 1(d) from the 2025 NCEA Level 2 Calculus paper for AS91262 — Apply calculus 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 AS91262.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise writing displacement equations, solving when they are equal, and answering in context. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.