Chapter 2: Motion and
Speed
Section 1: Describing Motion
Preface

Physics is a mathematical science – that
is, the underlying concepts and principles
have a mathematical basis. Throughout
the course of our study of physics, we will
encounter a variety of concepts which
have a mathematical basis associated with
them. While our emphasis will often be
upon the conceptual nature of physics, we
will give considerable and persistent
attention to its mathematical aspect.
Preface Cont.

The motion of objects can be described by
words – words such as distance,
displacement, speed, velocity, and
acceleration. These mathematical
quantities which are used to describe the
motion of objects can be divided into two
categories. The quantity is either a vector
or a scalar. These two categories can be
distinguished from one another by their
distinct definitions
Preface Cont.

Scalars are quantities which are fully
described by a magnitude alone.


Example: 5 m, 512 bytes, 6000 Calories
Vectors are quantities which are fully
described by both a magnitude and a
direction.

Example: 5 m/s, East and 45 miles, North
Introduction

Are distance and time important in
describing running events at the track and
field meets in the Olympics?

Why are they necessary?
Motion

Motion occurs when an object changes its
position

Question: How do we know whether
something has changed its position or not?

A reference point is needed to help
determine motion
Relative Motion

Motion is relative because the reference
point is arbitrary (relative, up to each
person)

Example: In reference to your desk, you
may not be moving. In reference to the
sun, you are moving about 30 km per
second
Distance

Distance is a scalar quantity which refers
to “how much ground an object has
covered” during its motion

Distance describes how far an object has
moved.

The SI unit, remember, is meters (m).
Longer distances can be measure using
kilometers (km) and shorter using
centimeters (cm)
Displacement

Displacement is a vector quantity which
refers to “how far out of place an object
is”

Displacement is the distance and direction
of an object’s change in position from the
starting point

Displacement always has a direction
attached to it
Some Examples


The diagram below shows the position of a crosscountry skier at various times. At each of the
indicated times, the skier turns around and reverses
the direction of travel. In other words, the skier
moves from A to B to C to D.
Use the diagram to determine the resulting
displacement and the distance traveled by the skier
during these three minutes.
Answer

The skier covers a distance of
(180m + 140m + 100m)= 420 m

The skier has a displacement of 140 m to
the right


A football coach paces back and forth along the
sidelines. The diagram below shows several of the
coach’s positions at various times. At each marked
position, the coach makes a “U-turn” and moves in the
opposite direction. In other words, the moves from
position A to B to C to D.
What is the coach’s resulting displacement and distance
of travel?
Answer

The coach covers a distance of
(35 yds + 20 yds + 40 yds)= 95 yards

The coach has a displacement of 55 yards
to the left
Speed

Speed is a scalar quantity which refers to
“how fast an object is moving.”

Speed is the distance an object travels per
unit of time.

A fast moving object has a high speed
while a slow moving object has a slow
speed. An object with no movement at all
has a zero speed.
Calculating Speed

Speed is relating distance traveled by the
time needed to do the traveling

Speed = Distance
Time
or
s=d
t
Example

If Mr. Kirby drives in his car from Dayton to
his home in Pennsylvania (approximately
550 miles away) in 8 hours, what is his
speed?

Answer: speed = 550 miles  68.75 mph
8 hours
All Types of Speed

Constant Speed occurs when an object is
neither slowing down or speeding up.

Changing Speed is not constant speed

Average Speed is TOTAL distance divided
by TOTAL time

Instantaneous Speed is speed at a given
point in time (your speedometer reading)
Velocity

Velocity is a vector quantity which refers
to “the rate at which an object changes its
position”

Velocity includes the speed of an object
and the direction of its motion

Imagine a person moving rapidly – one
step forward and one step back – always
returning to the starting position. While
this would result in a frenzy of activity,
their velocity would be zero.
Important concept to remember…

Because velocity depends on the direction
as well as speed, the velocity of an object
can change EVEN IF THE SPEED OF THE
OBJECT REMAINS CONSTANT.

Just like speed, you can have different
kinds of velocity.
Examples

The diagram below shows the position of a crosscountry skier at various times. At each of the indicated
times, the skier turns around and reverses the direction
of travel. In other words, the skier moves from A to B
to C to D.

Use the diagram to determine the average speed and
the average velocity of the skier during these three
minutes.
Answer

The skier has an average speed of
(420 m) / (3 min) = 140 m/min

The skier has an average velocity of
(140 m, right) / (3 min) = 46.7 m/min,
right
Example

A football coach paces back and forth along the
sidelines. The diagram below shows several of coach's
positions at various times. At each marked position, the
coach makes a "U-turn" and moves in the opposite
direction. In other words, the coach moves from
position A to B to C to D.

What is the coach's average speed and average
velocity?
Answer

The coach has an average speed of
(95 yd) / (10 min) = 9.5 yd/min

The coach has an average velocity of (55
yd, left) / (10 min) = 5.5 yd/min, left
Graphing Motion

Remembering there are different ways to
describe motion, using graphs to display
motion helps (hopefully) your
understanding of speed and velocity.
Graphing Essentials
•Time is plotted on the
horizontal axis (x-axis)
•Each axis must have a
scale that covers the range
of numbers you are working
with
Distance (m)
•Distance is plotted on the
vertical axis (y-axis)
•The slope of the line
representing the motion
of the object is the
speed.
Time (min)
An Example

Three swimmers decide to have a 30
minute workout. The broke up the
workout into three 10 minute periods.
The first swimmer swam 800 m during
each 10 – min period at a constant speed
of 80m/min. The second swimmer swam
at a constant speed of 60m/min for each
10 minute period. The third swimmer
swam 400 meters during the first 10
minutes at a constant speed, rested for
ten minutes, and then covered 800 meters
during the final 10 minutes.
2400
2200
2000
1800
•First Swimmer
•Second Swimmer
•Third Swimmer
Distance (m)
1600
1400
1200
1000
800
600
400
200
0
10
20
Time (min)
30