Mechanics
Extension 2 mechanics using calculus: Newton's laws and force resolution, rectilinear motion, simple harmonic motion, uniform circular motion, resisted motion, and projectile motion with air resistance.
Active lessons
6
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
6 of 6 active
Lesson 1
Forces and Motion on Inclined Planes
Apply Newton's three laws of motion and F = ma to model forces as vectors, resolve weight into components along and perpendicular to a smooth inclined plane, and analyse simple pulley systems.
Lesson 2
Rectilinear Motion with Calculus
Use v = dx/dt and a = dv/dt to find velocity and acceleration from a position function, recover position from acceleration using initial conditions, and interpret direction and speed from signs.
Lesson 3
Simple Harmonic Motion — Energy and Initial Conditions
Use x = a sin(nt + α) or x = a cos(nt + α) to identify amplitude, angular frequency and period, apply the energy equation v² = n²(a² − x²) to find speed at any position, and determine maximum speed and acceleration.
Lesson 4
Uniform Circular Motion
Apply v = rω and a = rω² = v²/r to find speed, centripetal acceleration, and centripetal force for objects in uniform circular motion, and connect angular velocity to period.
Lesson 5
Resisted Motion
Model horizontal resisted motion with ma = −kv and vertical resisted motion under gravity with ma = mg − kv, find terminal velocity, and solve the separable ODE for v(t) and x(t).
Lesson 6
Projectile Motion with Air Resistance
Analyse two-dimensional projectile motion with air resistance by solving decoupled horizontal and vertical ODEs, express velocity components as functions of time, and find the terminal speed in each direction.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.