This chapter examines vector function values for given values of the independent scalar variable. It utilizes the definitions of: average velocity, instantaneous velocity, average acceleration and instantaneous acceleration. The chapter outlines the steps involved in obtaining the derivative of a vector function from first principles. It discusses the derivative of a rotating vector of constant magnitude and the inertia! forces observed in accelerating and rotating frames of reference. The chapter explores the concept of a vector function of time and presents rules for differentiating sums and products of vector functions. It considers important examples of particle motion such as projectile motion and motion in a circle. The chapter describes applications to relative motion, including the derivation of inertial forces in accelerating and rotating frames of reference. It provides a review of ordinary scalar functions of a single scalar variable in order to establish some notation and definitions.