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.
