CK-12-Physics - Intermediate

2.1. Locating an Object: Distance and Displacement http://www.ck12.org

2.1 Locating an Object: Distance and Dis-

placement

Objectives

• Define scalar and vector.


• Define distance and displacement.


• Distinguish between distance and displacement.


• Graphically model distance and displacement.

Vocabulary

• displacement:The difference between final and initial positions.


• distance:The positive length between two points.


• position:The place of an object represented in the same way we might represent a point on a number line.


• scalar:Term used when referring only to magnitude.


• vector:Term used when referring to both magnitude and direction.

Equations

Distance:X=|P 1 −P 2 |+|P 2 −P 3 |+...

Displacement:∆x=Pf−Pi

Introduction

We begin our study of motion in the simplest terms possible- motion that takes place along a straight line. This is
called one-dimensional motion. A car traveling east, west, north, or south is an example of this kind of motion.

When we imagine a car moving along on a road, we think of the car as represented by a particle. We define the
position of a particle in the same way we would define the position of a point on a number line. Later on we will
take up the case of two-dimensional motion, like the motion of baseball through the air.

Scalars and Vectors

Consider the dashboard of a car shown inFigure2.2. It displays information about the motion of the car. The
odometer shows the miles driven by the car during its lifetime. The speedometer shows the instantaneous speed
of the car. These values describe amount, or size, or (as we say in physics) magnitude, but they do not include
information about the direction of the car’s motion.

In order to describe the motion of an object completely, two pieces of information are required

1. Magnitude (how far or how fast) and


2. Direction

In physics we use the termscalarwhen referring only to magnitude. Distance (i.e. 30 miles) and speed (i.e. 30
mph) are two examples of scalar quantities. We use the termvectorwhen referring to both magnitude and direction.
Two examples of vectors are: