Rectilinear Resisted Motion

Rectilinear resisted motion is part of the Mechanics topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-05). Starting from Newton’s second law, \(\sum F = m\ddot{x}\), this subtopic models a body travelling in a straight line while a resistance depending on its speed, such as \(kv\) or \(kv^2\), slows it down.

Students and teachers will cover setting up the equation of motion, integrating to find speed in terms of time or distance and position in terms of time, and problems such as how far a boat coasts after its engine stops — a challenging use of calculus in the HSC Extension 2 course.