Motion in Two Dimensions - Motion in a Plane

Up to this point, motion was confined to one straight line. Now the object's path is allowed to curve within a flat plane — the direction of the force on it need not coincide with the direction of its velocity at every instant, so velocity and acceleration can, and generally do, point in different directions from each other. Vector equations become essential rather than merely convenient.

All the definitions built up in section 3.2 (displacement, average and instantaneous velocity, average and instantaneous speed, acceleration) remain valid word-for-word in two dimensions — but two of them can now genuinely differ in a way they never could along a single line: the magnitude of the average velocity and the value of the average speed need not be equal, because the magnitude of the displacement need not equal the path length. A clean example: a particle that travels once around a circle and returns exactly to its starting point …