Introduction

Motion is simply a change in the position of an object with time. We see it everywhere — a toy car pushed along the floor, a cricket ball sent for a six, an aeroplane flying from one city to another — and these three everyday examples actually illustrate the three broad categories physicists use to classify motion.

Rectilinear motion is motion along a single straight line: the object's velocity and the force acting on it both lie along that one line, so a single signed number (positive or negative along the line) is enough to describe its position at any time. Motion in a plane (two-dimensional motion) happens when the object's path is confined to a flat surface but is no longer a straight line — the force on the object need not point along the same line as its velocity, so its motion has to be tracked along two perpendicular directions at once. Motion in space (three-dimensional motion) is the most general case, needing three independent directions.

You already met rectilinear motion in earlier standards, usually with plain positive/negative numbers for position, distance and speed. In this chapter we deliberately redo rectilinear motion using vector notation — writing position, displacement, velocity and acceleration as vectors with an explicit direction — because that same vector language is what makes two-dimensional motion tractable. Once rectilinear motion is expressed vectorially, extending every definition to a plane becomes close to automatic: you simply give each quantity an x-component and a y-component and treat the two directions independently.

With that vector toolkit built, the chapter studies projectile motion — the motion of an object launched with an initial velocity and afterwards moving only under gravity, restricted here to launches from level ground — as the chapter's worked example of two-dimensional motion. It also introduces uniform circular motion (an object moving at constant speed around a circular path), covering the basic ideas of period, angular speed and centripetal acceleration here, with a fuller treatment reserved for the next standard (rotational dynamics).