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Acceleration, Velocity, and Motion

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3 Acceleration
BEFORE YOU READ
Describe what happens to the speed of a bicycle as it goes uphill
and downhill.
WHAT YOU’LL LEARN
• how acceleration, time, and
velocity are related
• the three ways an object can
accelerate
• how to calculate acceleration
• the similarities and
differences between straight
line motion, circular motion,
and projectile motion
READ TO LEARN
Copyright © McGraw-Hill Education
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. Acceleration 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
its speed, its direction, or both.
When you think of acceleration, you might think of speeding up.
But an object that is slowing down also is accelerating. An object
that is changing direction is accelerating, too. Like velocity and
momentum, acceleration has a direction. The figure below shows
the three ways an object can accelerate. When the car is speeding
up, its acceleration and velocity are in the same direction. When
the car is slowing down, its acceleration is in the opposite
direction of its velocity. When the car changes direction, the
acceleration is not in the same direction or opposite direction as
the car’s velocity.
Speeding Up
Acceleration
Velocity
Slowing Down
STUDY COACH
Outlining As you read the
lesson, make an outline of the
important information in each
paragraph.
Get It?
1. Identify three ways that an
object can accelerate.
Changing Direction
Acceleration
Velocity
Velocity
Acceleration
Reading Essentials • Motion
33
Speed of Tamara’s Car
Moving at a
constant speed
25
Speed (km/h)
20
Slowing down to
enter parking lot
Speeding up
15
Slowing down
at a red light
10
5
Pulling out
of driveway
0
1
Parking
Stopped at
red light
2
3
4
5
6
7
Time (min)
Speed-time graphs and acceleration
When an object travels in a straight line and does not change
M02_023A-668304
direction, a graph of speed versus time can provide information
Venn Diagram
about an object’s acceleration. Look at the speed-time graph
Make the following trifold
above of Tamara’s car as she drives to the store. Remember that
Foldable to compare and
the slope of a line on a distance-time graph is the object’s speed.
contrast the characteristics
of acceleration, speed, and
The slope of a line on a speed-time graph is the object’s
velocity.
acceleration. For example, when Tamara pulls out of her
driveway, the car’s acceleration is 0.33 km/min2, which is equal to
Acceleration
the slope of the line from t = 0 to t = 0.5 min.
D Construct a
Speed
Velocity
APPLYING MATH
Acceleration is the rate of change in velocity. To calculate
acceleration, divide the change in velocity by the time interval
over which the change happened. The change in velocity is the
final velocity minus the initial velocity. If the object moves in a
straight line, the size of the change in velocity can be calculated
from the change in speed. Then, the acceleration of an object can
be calculated from the following equation.
acceleration (a) =
APPLYING MATH
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?
vf - vi
change in velocity (v)
_____
or
a
=
​​ 
t ​​
time (t)
In SI units, velocity has units of m/s and time has units of s, so
the SI unit of acceleration is m/s2. In some cases, your
calculations will result in a negative acceleration. The negative
sign means in the opposite direction. For example, an acceleration
of −10 m/s2 north is the same as 10 m/s2 south.
Reading Essentials • Motion
34
Copyright © McGraw-Hill Education
2. Use Variables Write what
M02_005A-685545
vf and vi mean.
Calculating acceleration
Motion in Two Dimensions
So far, we have only discussed motion in a straight line. But
most objects don’t move only in a straight line. Recall that we
cannot add measurements that are not in the same or opposite
directions. So, we will discuss motion in each direction separately.
For example, suppose a student walked three blocks north and
four blocks east. You could say the student walked north for three
blocks at 1 m/s and then walked east for four blocks at 2 m/s.
Recall that objects that change direction are accelerating. For
an object that is changing direction, its acceleration is not in the
same or opposite direction as its velocity. This means that we
cannot use the acceleration equation. Just as with displacement
and velocity, accelerations that are not in the same or opposite
directions cannot be directly combined.
Get It?
4. Explain why you cannot use
the acceleration equation
for an object that changes
direction.
APPLYING MATH
5. Explain Why is the
acceleration of an object
moving at a constant
velocity always 0?
Circular motion
Think about a horse’s horizontal motion on a carousel. The
horse moves in a circular path. Its speed remains constant, but
the horse is accelerating. That is because its direction of motion
changes. The change in the direction of the horse’s velocity is
toward the center of the carousel. The horse’s velocity is
perpendicular to the inward acceleration. Acceleration toward the
center of a curved or circular path is called centripetal
acceleration. In the same way, Earth experiences centripetal
acceleration as it orbits the Sun in a nearly circular path.
Copyright © McGraw-Hill Education
Projectile motion
If you have tossed a ball to someone, you have probably noticed
that thrown objects do not travel in straight lines. They curve
downward. That is why quarterbacks, dart players, and archers
aim above their targets. Anything that is thrown or shot through
the air is called a projectile. Earth’s gravity causes projectiles to
follow a curved path.
When you throw or shoot an object, like a ball or rubber band,
the force exerted gives the object a horizontal velocity. The
horizontal velocity is constant. The rubber band does not
accelerate horizontally. If there were no gravity, the rubber band
would move along a straight line.
However, when you release a rubber band, gravity causes it to
accelerate downward. The rubber band has an increasing vertical
velocity. The result of these two motions is that the rubber band
travels in a curve, even though its horizontal and vertical motions
are completely independent of each other.
Reading Essentials • Motion
35
Get It?
6. Define the term centripetal
acceleration.
If you were to throw a ball as hard as you could in a perfectly
horizontal direction, would it take longer to reach the ground
than if you dropped a ball from the same height? Surprisingly, it
will not. A thrown ball and a dropped ball will hit the ground at
the same time. Both balls travel the same vertical distance in the
same amount of time. However, the ball thrown horizontally
travels a greater horizontal distance than the ball that is dropped.
THINK IT OVER
7. Think Critically A car that
is slowing down is still
moving forward. Why is this
considered negative
acceleration?
Amusement park acceleration
Riding roller coasters in amusement parks can give you the
feeling of danger, but these rides are designed to be safe.
Engineers use the laws of physics to design amusement park rides
that are thrilling but harmless. Roller coasters are constructed of
steel or wood. Because wood is not as strong as steel, wooden
roller coasters do not have hills that are as high and as steep as
some steel roller coasters have.
The highest speeds and accelerations are usually produced on
steel roller coasters. Steel roller coasters can offer multiple steep
drops and inversion loops, which give the rider large
accelerations. As riders move down a steep hill or an inversion
loop, they will accelerate toward the ground due to gravity. When
riders go around a sharp turn, they are also accelerated. This
acceleration makes them feel as if a force is pushing them toward
the side of the car.
Copyright © McGraw-Hill Education
Reading Essentials • Motion
36
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