Chapter 11teachers.stjohns.k12.fl.us/moore-k/files/2014/05/Chapter-11-notes.pdf11.1 Distance and Displacement Chapter 11 ... 11.1 Distance and Displacement What is needed to ... is

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11.1 Distance and Displacement

Chapter 11Motion


How fast is the butterfly

moving? What direction is it

moving?

To describe motion, you

must state the direction the

object is moving as well as

how fast the object is

moving. You must also tell

its location at a certain time.


What is needed to describe motion

completely?

A frame of reference is a system of objects that

are not moving with respect to one another.

To describe motion accurately and

completely, a frame of reference is

necessary.

Choosing a Frame of Reference


How Fast Are You Moving?

How fast the passengers on a train are moving

depends on the frame of reference chosen to

measure their motion.

Relative motion is movement in relation to a

frame of reference.

• As the train moves past a platform, people standing

on the platform will see those on the train speeding

by.

• When the people on the train look at one another,

they don’t seem to be moving at all.



Which Frame Should You Choose?

• When you sit on a train and look out a window, a

treetop may help you see how fast you are

moving relative to the ground.

• If you get up and walk toward the rear of the

train, looking at a seat or the floor shows how

fast you are walking relative to the train.

• Choosing a meaningful frame of reference

allows you to describe motion in a clear and

relevant manner.



How are distance and displacement

different?

Distance is the length of the path between

two points. Displacement is the direction

from the starting point and the length of a

straight line from the starting point to the

ending point.

Measuring Distance

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Distance is the length of a path between two

points. When an object moves in a straight

line, the distance is the length of the line

connecting the object’s starting point and its

ending point.

• The SI unit for measuring distance is the meter

(m).

• For very large distances, it is more common to

make measurements in kilometers (km).

• Distances that are smaller than a meter are

measured in centimeters (cm).

Measuring Distance


To describe an object’s position relative to a

given point, you need to know how far away

and in what direction the object is from that

point. Displacement provides this information.

Measuring Displacements


Think about the motion of a roller coaster car.

• The length of the path along which the car has

traveled is distance.

• Displacement is the direction from the starting

point to the car and the length of the straight line

between them.

• After completing a trip around the track, the car’s

displacement is zero.

Measuring Displacements


How do you add displacements?

A vector is a quantity that has magnitude and

direction.

Add displacements using vector addition.

Combining Displacements


Displacement is an example of a vector.

• The magnitude can be size, length, or amount.

• Arrows on a graph or map are used to represent

vectors. The length of the arrow shows the

magnitude of the vector.

• Vector addition is the combining of vector

magnitudes and directions.



Displacement Along a Straight Line

When two displacements, represented by two

vectors, have the same direction, you can add

their magnitudes.

If two displacements are in opposite directions,

the magnitudes subtract from each other.


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A. Add the magnitudes of two displacement

vectors that have the same direction.

B. Two displacement vectors with opposite

directions are subtracted from each other.



Displacement That Isn’t Along a Straight Path

When two or more displacement vectors have

different directions, they may be combined by

graphing.



Measuring the resultant vector (the diagonal red

line) shows that the displacement from the boy’s

home to his school is two blocks less than the

distance he actually traveled.




















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The boy walked a total distance of 7 blocks.

This is the sum of the magnitudes of each

vector along the path.

The vector in red is called the resultant

vector, which is the vector sum of two or more

vectors.

The resultant vector points directly from the

starting point to the ending point.



The speed of an in-

line skater is usually

described in meters

per second. The

speed of a car is

usually described in

kilometers per hour.


How are instantaneous speed and average

speed different?

Speed

Average speed is computed for the entire

duration of a trip, and instantaneous speed

is measured at a particular instant.


Speed is the ratio of the distance an object

moves to the amount of time the object

moves.

The SI unit of speed is meters per second

(m/s).

Two ways to express the speed of an object

are average speed and instantaneous speed.

Speed


Average Speed

Sometimes it is useful to know how fast something

moves for an entire trip, even though its speed

may change during the trip.

Average speed, is the total distance traveled, d,

divided by the time, t, it takes to travel that

distance.

Speed

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Calculating Average Speed

While traveling on vacation, you measure the

times and distances traveled. You travel 35

kilometers in 0.4 hour, followed by 53 kilometers in

0.6 hour. What is your average speed?

Speed


Read and Understand

What information are you given?

Speed


Read and Understand


Total Distance (d) = 35 km + 53 km = 88 km

Total Time (t) = 0.4 h + 0.6 h = 1.0 h

Speed


Plan and Solve

What unknown are you trying to calculate?

What formula contains the given quantities

and the unknown?

Replace each variable with its known value.

Speed


Plan and Solve



and the unknown?


Speed


Look Back and Check

Is your answer reasonable?

Speed

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Look Back and Check


Yes, 88 km/h is a typical highway speed.

Speed


1. A person jogs 4.0 kilometers in 32 minutes,

then 2.0 kilometers in 22 minutes, and finally 1.0

kilometer in 16 minutes. What is the jogger’s

average speed in kilometers per minute?

Speed


1. A person jogs 4.0 kilometers in 32 minutes,

then 2.0 kilometers in 22 minutes, and finally 1.0

kilometer in 16 minutes. What is the jogger’s

average speed in kilometers per minute?

Answer:

Speed


2. A train travels 190 kilometers in 3.0 hours, and

then 120 kilometers in 2.0 hours. What is its

average speed?

Speed


2. A train travels 190 kilometers in 3.0 hours, and

then 120 kilometers in 2.0 hours. What is its

average speed?

Answer:

Speed


Instantaneous Speed

Sometimes you need to know how fast you are

going at a particular moment.

Instantaneous speed, v, is the rate at which an

object is moving at a given moment in time.

Speed

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The speedometer in a car

measures the car’s

instantaneous speed.

Note the scale markings

are given both in km/h and

miles per hour, mph.

Speed


How can you find the speed from a distance-

time graph?

Graphing Motion

The slope of a line on a distance-time graph

is speed.


A distance-time graph is a good way to

describe motion.

Slope is the change in the vertical axis value

divided by the change in the horizontal axis

value.

A steeper slope on a distance-time graph

indicates a higher speed.

Graphing Motion


Graphing Motion


Graphing Motion


Graphing Motion

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How are speed and velocity different?

Velocity

Velocity is a description of both speed and

direction of motion. Velocity is a vector.


Sometimes knowing only the speed of an

object isn’t enough. You also need to know

the direction of the object’s motion.

Together, the speed and direction in which an

object is moving are called velocity.

Velocity


A cheetah’s speed may be as fast as 90

km/h. To describe the cheetah’s velocity, you

must also know the direction in which it is

moving.

Velocity


Vectors can be used to show changes in

motion.

• Vectors of varying lengths, each vector

corresponding to the velocity at a particular

instant, can represent motion.

• A longer vector represents a faster speed, and

a shorter one a slower speed.

• Vectors point in different directions to represent

direction at any moment.

Velocity


As the sailboat’s direction

changes, its velocity also

changes, even if its speed

stays the same.

Velocity


How do velocities add?

Combining Velocities

Two or more velocities add by vector

addition.

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Sometimes the motion of an object involves

more than one velocity.

If a boat is moving on a flowing river, the

velocity of the river relative to the riverbank

and the velocity of the boat relative to the

river combine.

They yield the velocity of the boat relative to

the riverbank.



The velocity of the boat relative to the

riverbank is a combination of the relative

velocities of the boat and the river.



The velocity of the boat relative to the

riverbank is a combination of the relative

velocities of the boat and the river.



How are changes in velocity described?

The rate at which velocity changes is called

acceleration.

Scientists can perform artificial

transmutations by bombarding atomic nuclei

with high-energy particles such as protons,

neutrons, or alpha particles.

What Is Acceleration?


Changes in Speed

• In science, acceleration applies to any change in

an object’s velocity.

• Acceleration can be caused by positive

(increasing) change in speed or by negative

(decreasing) change in speed.

• Deceleration is an acceleration that slows an

object’s speed.



Free fall is the movement of an object toward

Earth solely because of gravity.

The unit for velocity is meters per second. The

unit for acceleration, then, is meters per second

per second. This unit is typically written as meters

per second squared (m/s2).

Objects falling near Earth’s surface accelerate

downward at a rate of 9.8 m/s2.


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Each second an object is in

free fall, its velocity

increases downward by 9.8

meters per second.

The change in the stone’s

speed is 9.8 m/s2, the

acceleration due to gravity.

What Is Acceleration?t = 0 s

v = 0 m/s

t = 1 s

v = 9.8 m/s

t = 2 s

v = 19.6 m/s

t = 3 s

v = 29.4 m/s


Changes in Direction

Acceleration can be the result of a change in

direction at constant speed, for example, riding a

bicycle around a curve.



A horse on the carousel is traveling at a constant

speed, but it is accelerating because its direction

is constantly changing.



Changes in Speed and Direction

Sometimes motion is characterized by changes in

both speed and direction at the same time.

Passengers in a car moving along a winding road

experience rapidly changing acceleration.

The car may enter a long curve at the same time

that it slows. The car is accelerating both because

it is changing direction and because its speed is

decreasing.



A roller coaster produces acceleration due to

changes in both speed and direction.



Constant Acceleration

The velocity of an object moving in a straight line

changes at a constant rate when the object is

experiencing constant acceleration.

• Constant acceleration is a steady change in

velocity.

• An airplane’s acceleration may be constant during a

portion of its takeoff.


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Constant acceleration during takeoff results in

changes to an aircraft’s velocity that is in a

constant direction.



How can you calculate acceleration?

You calculate acceleration for straight-line

motion by dividing the change in velocity by

the total time.

Calculating Acceleration


Acceleration is the rate at which velocity changes.

Vi is the initial velocity, vf is the final velocity, and t

is total time.



If the velocity increases, the acceleration is

positive. If the velocity decreases, the

acceleration is negative.

• If you are coasting downhill on a bicycle, your

velocity increases, and your acceleration is positive.

• If you continue coasting on level ground, your

velocity decreases, and your acceleration is

negative.



Acceleration and velocity are both vector

quantities.

• To determine a change in velocity, subtract one

velocity vector from another.

• If the motion is in a straight line, velocity can be

treated as speed, and acceleration is the change in

speed divided by the time.




A ball rolls down a ramp, starting from rest. After 2

seconds, its velocity is 6 meters per second. What

is the acceleration of the ball?


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Read and Understand


Balancing Equations


Read and Understand


Balancing Equations


Plan and Solve



and the unknown?

Balancing Equations


Plan and Solve



and the unknown?

Balancing Equations


Plan and Solve


Balancing Equations


Plan and Solve


Balancing Equations

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Look Back and Check


Balancing Equations


Look Back and Check


Objects in free fall accelerate at a rate of 9.8 m/s2.

The ramp is not very steep. An acceleration of 3 m/s2

seems reasonable.

Balancing Equations


1. A car traveling at 10 m/s starts to decelerate

steadily. It comes to a complete stop in 20

seconds. What is its acceleration?

Describing Ionic Compounds


1. An airplane travels down a runway for 4.0

seconds with an acceleration of 9.0 m/s2. What is

its change in velocity during this time?



1. An airplane travels down a runway for 4.0

seconds with an acceleration of 9.0 m/s2. What is

its change in velocity during this time?

Answer:

(vf – vi) = at = (9.0 m/s2)(4.0 s) = 36 m/s



2. A child drops a ball from a bridge. The ball

strikes the water under the bridge 2.0 seconds

later. What is the velocity of the ball when it

strikes the water?


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2. A child drops a ball from a bridge. The ball

strikes the water under the bridge 2.0 seconds

later. What is the velocity of the ball when it

strikes the water?

Answer:

vi = 0; vf = at = (9.8 m/s2)(2.0 s) = 20 m/s



3. A boy throws a rock straight up into the air. It

reaches the highest point of its flight after 2.5

seconds. How fast was the rock going when it left

the boy’s hand?



3. A boy throws a rock straight up into the air. It

reaches the highest point of its flight after 2.5

seconds. How fast was the rock going when it left

the boy’s hand?

Answer:

vf = 0; vi = –at = –(9.8 m/s2)(2.5 s) = –25 m/s

(The minus sign indicates that the velocity is in

the direction opposite the acceleration.)



How does a speed-time graph indicate

acceleration?

The slope of a speed-time graph is

acceleration.

Graphs of Accelerated Motion


You can use a graph to calculate acceleration.

Graph speed on the vertical axis and time on the

horizontal axis.

The slope is change in speed divided by change

in time, which is equal to the acceleration.



The skier’s acceleration is positive. The

acceleration is 4 m/s2.


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Speed-Time Graphs

Constant acceleration is represented on a speed–

time graph by a straight line. The slope of the line

is the acceleration.

The graph is an example of a linear graph, in

which the displayed data form straight-line parts.



Constant negative acceleration decreases speed.

• On a speed-time graph of a bicycle slowing to a

stop, a line sloping downward represents the bicycle

decelerating.

• The change in speed is negative, so the slope of the

line is negative.



The biker moves at a constant speed and then

slows to a stop.



Distance-Time Graphs

Accelerated motion is represented by a curved

line on a distance-time graph.

In a nonlinear graph, a curve connects the data

points that are plotted.



A distance-time graph of accelerated motion

is a curve. The data in this graph are for a ball

dropped from rest toward the ground.



Compare the slope of the curve during the first

second to the slope during the fourth second. An

increasing slope means that the speed is

increasing.


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What is instantaneous acceleration?

Instantaneous acceleration is how fast a

velocity is changing at a specific instant.

Instantaneous Acceleration


Acceleration is rarely constant, and motion is

rarely in a straight line.

• Acceleration involves a change in velocity or

direction or both, so the vector of acceleration can

point in any direction.

• The vector’s length depends on how fast velocity is

changing.

• For an object that is standing still, the acceleration

vector is zero.

Instantaneous Acceleration

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Chapter 11teachers.stjohns.k12.fl.us/moore-k/files/2014/05/Chapter-11-notes.pdf11.1 Distance and Displacement Chapter 11 ... 11.1 Distance and Displacement What is needed to ... is