# PHYS 2211 Module 4.1

## Displacement and Velocity Vectors

4.1 Displacement and Velocity Vectors

### Learning Objectives

By the end of this section, you will be able to:

• Calculate position vectors in a multidimensional displacement problem.
• Solve for the displacement in two or three dimensions.
• Calculate the velocity vector given the position vector as a function of time.
• Calculate the average velocity in multiple dimensions.

### Position and Displacement Vectors in Three Dimensions

The position vector from the origin of the coordinate system to a point is

If the particle is moving, the variables xy, and z are functions of time (t): x(t), y(t), and z(t).

The displacement vector  is found by subtracting  from :

### Velocity and Average Velocity in Three Dimensions

In the previous chapter we found the instantaneous velocity by calculating the derivative of the position function with respect to time. We can do the same operation in two and three dimensions, but we use vectors. The instantaneous velocity vector is

We can also write the instantaneous velocity vector in vector notation:

where , , and .

Practice!

Discuss!

Consider how you would answer these questions. Then bring this to class for a group discussion.

The position of a particle is

(a) Determine its velocity and acceleration as functions of time.

(b) What are its velocity and acceleration at time t = 0?