Velocity & Acceleration as Functions of x

Velocity and acceleration as functions of displacement begins the Mechanics topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-05). This subtopic shows that acceleration can be written as \(\dfrac{dv}{dt}\), \(v\dfrac{dv}{dx}\) or \(\dfrac{d}{dx}\left(\dfrac{1}{2}v^2\right)\), the last two being useful when velocity \(v\) depends on displacement \(x\).

Students and teachers will cover moving between acceleration, velocity and displacement when acceleration is given as a function of \(x\) or of \(v\), integrating to find \(v^2\), \(x\) or \(t\) — the calculus foundation for every motion model in the HSC Extension 2 course.