Objectives
- To understand how the velocity vector of a vector valued function of one variable is defined.
- To identify the velocity vector and its geometric properties relating to a curve in space.
Section 5.2 The Velocity Vector
Subsection 5.2.1 The Velocity Vector
This lesson defines and explains the measurement of velocity as a vector and speed as a scalar. The velocity vector is motivated by looking at the limit of secant vectors and the relation to the definition of derivative for vector valued functions. The geometry of the velocity vector is explained as being tangent to the curve and for several examples, the two dimensional speed graph can be compared to the changing of the magnitude of the velocity vector. All four of the base examples used in the vector valued functions of one variable lessons are animated and available for exploration at the end of the lesson.
