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 derives the expressions for acceleration \(\dfrac{dv}{dt}\), \(v\dfrac{dv}{dx}\) and \(\dfrac{d}{dx}\left(\dfrac{1}{2}v^2\right)\), where the velocity \(v\) is a function of displacement \(x\).

Students and teachers will cover how to solve problems where velocity and acceleration are expressed in terms of displacement, and where acceleration is expressed in terms of velocity — the calculus foundation for every motion model in the HSC Extension 2 course.