The earth and other planets travel around the sun. A bus carries you from home to school. Water flows in the river, and snow falls in the winter. All these events have one common thing: in each event one object moves from one place to another. In other words, through each of these events, an object changes its position. Such an action is called motion.

Basic Factors of a Motion: Displacement, Distance, and Elapsed Time
The length an object moves through its motion is called the distance. For example, when you move across a street, the distance covered is the width of the street.
In the figure below, a person starts running from point A, through the paths AB, BC, and CD and stops at D. Thus, the distance covered through this motion is
AB + BC + CD.

The linear distance between the original position and the final position of an object is called the displacement of the object in motion. For example, in the figure above, the displacement of the person is equal to the length AD, which is different (shorter) than the distance he traveled.

If a motion is on a straight line, we can measure the path of the motion on the x-axis and denote the starting and the ending points of the motion by the points x₁ and x₂, respectively. Then, denoting the distance covered by an object by ∆x, we can set the formula below for the distance. [The notation ∆x (delta) does not mean that and x are multiplied; rather it represents the magnitude of change (∆ ) in the variable x. In physics, we usually use the symbol ∆ to indicate the magnitude of increase or decrease in a quantity.]

The motion of an object takes time to occur. That is, moving from one place to another happens in the course of time. Such a time interval is called the elapsed time.

For example, assume that your school bus picks you up at 7:20 AM and arrives at school at 7:48 AM. Then this motion, that is your movement from home to school, takes place between 7:20 and 7:48 AM. The difference between these times indicates the elapsed time of your motion from home to school.

Elapsed Time = 7:48 AM ─ 7:20 AM = 28 minutes

We usually denote the starting time of a motion by t₁ and ending time by t₂, and the elapse time by ∆t. Then,

Types of Motions
The motion of most objects is usually characterized as Rectilinear or Curvilinear. In this lesson, we will focus on rectilinear motion only, and will explore curvilinear motion in high school physics.
When an object moves on a straight path in any direction, its motion is called linear.
Driving a car on a straight road, running on a straight track, or a snow flake falling down is a rectilinear motion.

Practice 1. On the graph below, the route of motion of an object starting from the point M and stopping at the point N is shown. Find the distance and the displacement covered by the object from M up to N.

Solution. The distance covered by the object is MA + AB + BN.
Replace the variables in this expression with the measures given.

Distance MN = 12 ft. + 23 ft. + 9 ft. = 44 ft.

The displacement of the object is equal to the distance between the original position M and the final position N. This length is the same as MN which is 44 ft. Thus, in this case, the distance and the displacement are the same.

Practice 2. In order to move from the town A to the town D, a driver must drive through the routes AB, BC, and CD. If a person moves from A to D, what are the distance and the displacement in this movement?

Solution. The distance traveled by moving from A to D is equal to AB + BC + CD. Replacing the names of these routes with the lengths we find
Distance between A and D = AB + BC + CD
                                                = 23 miles + 16 miles + 21 miles
                                                = 60 miles


Experiments for Home and Classroom

For experiments related to the concept of motion, see the following web pages:

http://www.glencoe.com/sec/science/internet_lab/olc.php?olcChapter=801

http://members.tripod.com/qldscienceteachers/junior/expt/physics_motion.html

http://physics.about.com/od/mechanicsexp/a/weightofair.htm

http://sprott.physics.wisc.edu/demobook/chapter1.htm

Now let's do Practice Exercise 1-1 (top). Choose printer friendly or online exercises. Printer friendly version requires the Adobe Acrobat Reader 5. Click HERE to obtain a free copy.