02 — Kinematics in Two Dimensions Worked Examples

Build confidence with vector motion through six fully worked examples across 18 illustrated pages.

Part of the Premium Mechanics Series from Phi Advanced STEM Studies, this resource shows how to choose a method, set up the physics and carry the calculation through to a physically meaningful answer. Each question is followed by a full solution. Try the question first, then compare your reasoning with the model approach.

WHAT YOU WILL WORK THROUGH

• A survey robot’s route: position, displacement, average velocity and average speed.
• Changes in a velocity vector: speed, direction and average acceleration.
• Constant acceleration in a plane: resolving vectors and reconstructing motion.
• A path crossing the same line twice: times, velocities and the turning point.
• Parametric and Cartesian paths: eliminating time and keeping the physical domain.
• Calculus extension: integrating time-dependent acceleration and finding a path gradient.

WHAT MAKES THIS RESOURCE USEFUL

• Six multi-part examples with step-by-step reasoning and clearly identified final answers.
• Labelled diagrams, chosen axes and explicit modelling assumptions.
• Explanations of signs, directions, units and checks on the results.
• Progression from more guided work towards greater independence in choosing a method.

MATHEMATICAL LEVEL
Examples 1–5 use algebra and trigonometry. Parametric elimination is an algebraic bridge whose syllabus emphasis varies. Example 6 is a labelled calculus extension using vector integration and the path-gradient relation.

CURRICULUM RELEVANCE
Supports component and vector methods used in international upper-secondary mechanics, including A-level and AP Physics, with relevant preparation for IB vector-based motion. The calculus example is intended for AP Physics C, mathematics mechanics and university preparation. Requirements vary by course.

WHAT YOU RECEIVE
The English-language 18-page Worked Examples PDF, containing six fully worked, multi-part examples, plus the matching Instructor Question Map PDF. Two sample-page images are also included.

The separate Guided Self-Study Notes and Practice Problems and Fully Worked Solutions are not included. No editable source files, multilingual glossary, tutoring or personal feedback are included.

These independently produced educational support materials are not an official publication or endorsement by any examination board.