Most real-world kinematics problems involve the motion of objects in two and three dimensions. (This should come as no surprise, since we do live in a three-dimensional world.) Fortunately, most of the equations we derived in the previous SparkNote on one-dimensional motion) can be easily generalized to the two- and three-dimensional cases. The prescription for doing this is simple: instead of treating x(t), v(t), and a(t) as scalar-valued functions for position, velocity, and acceleration, we will reinterpret these functions as being vector-valued. In other words, instead of the value of x(t) at a particular point in time being a number (or scalar), the value of the function at that point will be a vector.
This section will be divided into two parts. The first part will be devoted to understanding position, velocity, and acceleration as vector quantities, and rewriting all of the major kinematics equations from one-dimensional motion into vector form. The second part will focus on studying some of the most standard applications of this formalism, using examples involving motion with constant acceleration. Projectile motion will be the main focus here. In order to avoid confusion, vectors will be denoted by bold letters (to distinguish them from scalars) throughout this section.