Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
36 CHAPTER 2 Motion
Describe what happens to the speed of a bicycle as it goes
uphill and downhill.
Before You Read
Read to Learn
Velocity and Acceleration
A car sitting at a stoplight is not moving. When the light
turns green, the driver presses the gas pedal and the car starts
moving. The car moves faster and faster. Speed is the rate
of change of position. A
cceleration is the rate of change of
velocity. When the velocity of an object changes, the object
is accelerating.
Remember that velocity is a measure that includes both speed
and direction. Because of this, a change in velocity can be either
a change in how fast something is moving or a change in the
direction it is moving. Acceleration means that an object
changes it speed, its direction, or both.
How are speeding up and slowing down
described?
When you think of something accelerating, you probably
think of it as speeding up. But an object that is slowing down
is also accelerating. Remember that acceleration is a change in
speed. A car that is slowing down is decreasing its speed. It is
also accelerating, because its speed is changing.
Imagine a car being driven down a road. If the speed is
increasing, the car has positive acceleration. When the car
slows down, the speed decreases. The decreasing speed is called
negative acceleration. In both cases, the car is accelerating,
but one acceleration is positive and one is negative.
chapter
Motion
section ● Acceleration
2
3
What You’ll Learn
■
how acceleration, time,
and velocity are related
■
the different ways an
object can accelerate
■
how to calculate
acceleration
■
the similarities and
differences between
straight line motion,
projectile motion, and
circular motion
Outlining As you read the
section, make an outline of
the important information in
each paragraph.
Study Coach
●
D Construct a Venn
Diagram
Make the following
trifold Foldable to compare and
contrast the characteristics of
acceleration, speed, and velocity.
Acceleration
Velocity
Speed
026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 36 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File
P rinter P DF
Reading Essentials 37
Acceleration has direction, just like velocity. In the figure
below, both cars are accelerating because their speeds are
changing. When a car’s acceleration and velocity are in the
same direction, the speed increases and the acceleration is pos-
itive. Car A has positive acceleration. When a car is slowing
down, the acceleration and velocity are in opposite directions.
The acceleration is negative. Car B has negative acceleration.
Does changing direction affect acceleration?
A change in velocity is either a change in an object’s speed
or its direction. When a moving object changes direction, its
velocity changes and it is accelerating. The speed of a horse
moving around on a carousel remains constant, but it is
constantly changing direction. So, the horse is accelerating.
How do you calculate acceleration?
Acceleration is the rate of change in velocity. To calculate
acceleration, you first find the change in velocity. To find
change in velocity subtract the beginning velocity of an object
from the velocity at the end of its movement. Beginning
velocity is called the initial velocity, or
v
i
. Velocity at the end is
called the final velocity, or
v
f
.
change in velocity ⫽ final velocity ⫺ initial velocity
⫽ v
f
⫺ v
i
If motion is in a straight line, the change in speed can be
used to calculate the change in velocity. The change in speed
is the final speed minus the initial speed.
To find acceleration, divide the change in velocity by the
length of time during which the velocity changed.
acceleration
(a) ⫽
ᎏ
chang
t
e
im
in
e
v
(
e
t)
locity
ᎏ
or a ⴝ
ᎏ
(v
f
ⴚ
t
v
i
)
ᎏ
The SI unit for velocity is meters per second (m/s). To find
acceleration, velocity is divided by the time in seconds (s).
So, the unit for acceleration is m/s
2
.
Velocity
Acceleration
Car A
Velocity
Acceleration
Car B
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Describe the acceleration of
the cars in each figure.
Picture This
2. Use Variables Write what
v
f
and v
i
mean.
3. Calculate Suppose a bird
takes off from a tree and
flies in a straight line.
It reaches a speed of 10 m/s.
What is the change in the
bird’s velocity?
Applying Math
026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 37 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File
P rinter P DF
38 CHAPTER 2 Motion
How is positive acceleration calculated?
How is the acceleration of an object that is speeding up
different from that of an object that is slowing down? The accel-
eration of an object that is speeding up is always positive. The
acceleration of an object that is slowing down is always negative.
Suppose an airplane is sitting at the end of a runway. The
plane takes off and moves down the runway. It takes 20 s for
the plane to travel from one end of the runway to the other.
When the airplane reaches the end of the runway, it is travel-
ing 80 m/s. The airplane is traveling in a straight line. The ini-
tial velocity of the plane is 0 m/s and the final velocity of the
plane is 80 m/s. The time is 20 seconds. The acceleration for
the plane can be calculated as follows:
a ⫽
ᎏ
(v
f
⫺
t
v
i
)
ᎏ
⫽
ᎏ
(80 m/s
20
⫺
s
0 m/s)
ᎏ
⫽ 4 m/s
2
The airplane is speeding up as it goes down the runway.
The final speed is greater than the initial speed. The accelera-
tion is positive.
How is negative acceleration calculated?
Now imagine a skateboarder moving in a straight line. The
skateboarder is moving at a speed of 3 m/s. It takes the per-
son 2 s to come to a stop. The initial velocity is 3 m/s and the
final velocity is 0 m/s. The total time is 2 seconds. The calcu-
lation for the skateboarder’s acceleration is as follows:
a ⫽
ᎏ
(v
f
⫺
t
v
i
)
ᎏ
⫽
ᎏ
(0 m/s
2
⫺
s
3 m/s)
ᎏ
⫽⫺1.5 m/s
2
The skateboarder is slowing down. The final speed is less
than the initial speed. The acceleration has a negative value.
Amusement Park Acceleration
Roller coasters are exciting rides. People who design roller
coasters use the laws of physics. The steep drops and loops of
steel roller coasters give the rider large accelerations. When
riders move down a steep hill, gravity will cause them to
accelerate toward the ground. When riders go around a sharp
turn, they are also accelerated. This acceleration makes them
feel as if a force were pushing them toward the side of the car.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Think Critically A car that is
slowing down is still moving
forward. Why is this consid-
ered negative acceleration?
4. Explain Why is the acceler-
ation of an object moving
at a constant velocity
always 0?
Applying Math
026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 38 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File
P rinter P DF
Reading Essentials 39
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Review the term and its definition in the Mini Glossary. Explain why a change in velocity
affects acceleration.
2. Complete the chart to organize information about how acceleration is calculated.
3. As you read the section, you made an outline describing the points covered in
each paragraph. How did you decide what to write as the major points in your outline?
Study Coach
Which is greater in
negative acceleration,
initial or final velocity?
Which is greater in
positive acceleration,
initial or final velocity?
The formula for
acceleration:
acceleration: the rate of change in velocity centripetal acceleration: acceleration toward the center of
a curved or circular path
After You Read
Mini Glossary
End of
Section
026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 39 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File
P rinter P DF
