Kinematics (M2) Topic Review summary

Key learning points

• Use calculus forms $a=\\frac{dv}{dt}=v\\frac{dv}{ds}$ fluently.
• Integrate acceleration to recover velocity and displacement with constants.
• Projectiles: horizontal motion uniform; vertical uses SUVAT/gravity.
• Relative motion ideas may appear in connected settings.
• Vector kinematics in a plane with $\\mathbf{i},\\mathbf{j}$ components.

Worked example 1 — Chain

$a=v\\frac{dv}{ds}$ use-case.

Working

Separate and integrate.

Worked example 2 — Projectile cue

Horizontal component of velocity.

Working

No horizontal acceleration (no air resistance).

Worked example 3 — Use calculus forms a=\\\dv{dt}=v\\\dv{ds}

Use calculus forms $a=\\\\frac{dv}{dt}=v\\\\frac{dv}{ds}$ fluently.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Integrate acceleration to recover velocity

Apply this idea from the Topic Review: Integrate acceleration to recover velocity and displacement with constants.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.