B

1 Motion, Acceleration, and Forces

Have you ever been on a roller coaster? You can feel the steepdrops and quick turns in your body. Write how it feels to travelup a steep hill slowly and then to go down the other side quickly.

Before You Read

Read to LearnMotion

Every day you see things around you in motion. Cars andtrucks move along streets. People walk and run and move indifferent places. They move in different directions and at different speeds. How can you describe the motion of peopleand objects? You could say they are fast or slow. In addition to speed, you can talk about the direction something is moving. You also can describe the way the speed or directionis changing.

How are motion and position related?You don’t need to see something move to know that it has

moved. Suppose you see a mail truck stopped at a mailbox. Alittle while later, you see the same mail truck farther down thestreet, next to a tree. You know the truck moved because itsposition relative to the mailbox has changed. Motion occurswhen an object changes position.

What is a reference frame?To measure the position of an object, you must pick a

reference frame. A reference frame is a group of objects that donot move relative to each other. For example, on a street,buildings, mailboxes, and trees make up a reference frame. Onepoint in the frame is chosen as the reference point. The positionis the distance and direction of the mail truck from the point ofreference.

Motion, Acceleration, and Forcessection ! Describing Motion1

What You’ll Learn" the difference between

displacement anddistance

" the difference betweenspeed and velocity

" how to graph motion

Identify the Main PointHighlight the main point in each paragraph in this section.Then highlight a detail or example that helps explain thepoint.

!A Find Main Ideas Asyou read this section, make thefollowing Foldable to help youidentify the main ideas aboutmotion.

Motion andPosition

RelativeMotion

DisplacementDistance

2

What is relative motion?Imagine you are sitting in a moving car. Are you moving? It

depends on the reference frame. If the car is your referenceframe, then you are not moving. But you definitely are movingrelative to the ground. Earth is moving around the Sun at aspeed of 30 km/s. So are you moving when you are in the car?It depends on whether your reference point is the car, the road,or the Sun. There is no reference frame that is at rest comparedto all other reference frames. An object’s motion is relative to achosen reference frame.

How do distance and displacement differ?Distance is how far something has moved. In the figure

below, the runner jogged 50 m to the north, turned around,and jogged 30 m to the south. The total distance is 80 m. Sheis now 20 m from the starting point. Displacement is the distance and direction of an object’s final position relative toits starting point. The runner’s displacement is 20 m north.

Displacement includes a size and a direction. This is knownas a vector. A vector is a quantity specified by size and direction.

SpeedSpeed is the distance an object travels per unit of time. To

describe how fast something is moving, you need to know howfar it travels in a certain amount of time. In SI units, the unit ofspeed is meters per second (m/s).

Usually an object’s speed changes as it moves. But you canfind the speed at a single instant. Instantaneous speed is thespeed of an object at a single instant of time. A car’s speedometer measures the instantaneous speed of the car.

2. Describe another waya runner could have adisplacement of 20 mnorth.

Picture This

1. Calculate A train traveling at a constant speedcovers a distance of 960meters in 30 s. What is thetrain’s speed? Show yourwork.

Applying Math

Distance from startingline is 20 m.

30 m

50 m

40 m

30 m

20 m

10 m

50 m

Displacement = 20 m north of starting lineDistance traveled = 50 m + 30 m = 80 m

N

3 Motion, Acceleration, and Forces

How do you calculate average speed?You can find an object’s average speed to tell how quickly

an object traveled over an entire distance. The average speedof any object is the total distance traveled divided by the totaltravel time. You can find average speed by using this equation:

average speed (in meters/seconds) = total distance (in meters)total time (in seconds)

–v = dt

The units for average speed are a distance unit divided by atime unit. In addition to m/s, other units, such as kilometersper hour (km/h), can be used.

VelocitySuppose you hear that a storm is approaching. The storm is

traveling at a speed of 20 km/h and is 100 km east of yourlocation. Do you have enough information to know whetherthe storm will reach you?

Knowing only the speed and location of the storm is notenough information to decide if the storm will reach you. Thespeed tells you how fast the storm is moving. To find theanswer, you also need to know the direction the storm ismoving. In other words, you need to know the velocity of thestorm. Velocity is the speed of an object and the direction it ismoving. Like displacement, velocity is a vector that has a sizeand a direction. The size of an object’s velocity is the object’sspeed.

How do speed and direction affect velocity?To help you understand velocity, think about two escalators.

One escalator is moving upward at the same speed that theother escalator is moving downward. The two escalators aregoing the same speed, but they are going in different directions.They each have a different velocity. If the second escalatorwere moving upward, both elevators would have the samevelocity.

Velocity depends on both speed and direction. Because ofthis, an object moving at a constant speed will have a changingvelocity if it changes direction. As a race car goes around anoval track, the direction in which the car is moving changes.This means that the velocity of the car is changing. An objecthas constant velocity if neither its speed nor its directionchanges. The light from a laser beam travels at a constantvelocity.

4. Explain why the velocityof a race car going at aconstant speed around anoval track is changing.

FC

AT FOCUSFC

AT FOCUS

Benchmark Check

SC.C.1.4.1

3. Explain Whatterm describes the total distance an object hastraveled divided by itstotal travel time?

#

4

Graphing MotionA distance-time graph shows the motion of an object over

time. The graph below shows the motion of three swimmersduring a 30-min workout. The line for Mary is straight. Thismeans that she swam at a constant speed. Her speed was 80 m/min for the whole 30 min.

The line for Kathy is also straight. Kathy also swam at aconstant speed. Her speed was 60 m/min for the whole 30 min.Notice that Julie’s line is not straight. Julie did not swim at aconstant speed. During part of the practice, Julie rested andher line is horizontal. It has zero slope. During the last part ofthe practice, Julie swam as fast as Mary. That part of Julie’sline has the same slope as Mary’s line.

The steepness of the line is called the slope. The slope of aline on the graph is the speed. A steeper slope means a greaterspeed. Mary was swimming faster than Kathy, so the slope ofMary’s line is steeper than the slope of Kathy’s line.

Plotting Graphs A distance-time graph plots data for distance and time. The distance traveled is plotted on thevertical axis. Time is plotted on the horizontal axis. Eachaxis has a scale, or a series of numbers, for the data range.

Mary swam the farthest during the practice, 2,400 m. So,the vertical scale must go to 2,400. The practice was 30 minlong, so the horizontal axis must go to 30. Each axis is dividedinto equal parts. When each axis is finished, the data pointsare plotted on the graph. Then the data points for each swimmer are connected with a line.

Graphing Motion

Dis

tanc

e (m

)

0

200

400

2,400

2,200

2,000

1,800

1,600

1,400

1,200

1,000

800

600

Time (min)10 20 300

Mary swam at a constant speed of 80m/min. Her speed was the fastest,so this line has the steepest slope.

At first Julieswam witha speed of40 m/min.The slope ofthis line isless thanKathy‘s line.

Kathy swam with aconstant speed of60 m/min. The slopeof this line is less thanthe slope of Mary’s line.

Here Julie‘s speed was80 m/min. The slope ofthis line is the same asMary‘s line.

Here Julie‘s speed was 0 m/min.The slope of this line is 0 m/min.

5. Explain why the slopesare different for eachswimmer.

Applying Math

6. Identify Highlight theparts of the two lines thathave the same slope. Whyare the slopes the same?

Picture This

.

5 Motion, Acceleration, and Forces

1. Review the terms and their definitions in the Mini Glossary. What is the differencebetween average speed and instantaneous speed?

2.

Answer:

Question:

average speed: the total distance traveled in a unit of timedisplacement: the distance and direction that something

moved from a starting pointinstantaneous speed: the speed of an object at one point

in time

speed: the distance an object travels in an amount of timevector: a quantity that is specified by size and directionvelocity: a measure of the speed of an object and the direction

it is traveling

After You ReadMini Glossary

Go back to page one and now answer "Before You Read" section applying what you have learned.

6

Before You Read

Read to Learn

What You’ll Learn" how acceleration, time,

and velocity are related" how positive and

negative accelerationaffect motion

" how to calculateacceleration

Describe what happens to the speed of a bicycle as it goesuphill and downhill.

Acceleration, Speed, and VelocityA car sitting at a stoplight starts moving when the light

turns green. When the car started moving, its velocityincreased and it was accelerating. Acceleration is the changein velocity divided by the time for the change to occur.

Remember that velocity is a vector that includes both speedand direction. Because of this, a change in velocity can be eithera change in how fast something is moving or a change in thedirection it is moving. Acceleration means that an objectchanges it speed, its direction, or both.

What do direction changes affect?Acceleration has direction, just like velocity. In the figure

belows, both cars are accelerating because their speeds arechanging.

Motion, Acceleration, and Forcessection ! Acceleration2

Outline As you read thesection, make an outline of the important information ineach paragraph.

Study Coach

!B Construct a VennDiagram Make the followingtrifold Foldable to compare andcontrast the characteristics ofacceleration, speed, and velocity.

Acceleration

VelocitySpeed

Velocity

Acceleration

Car A

Velocity

Acceleration

Car B

7

Direction Changes When a car’s acceleration and velocityare in the same direction, the speed increases and the acceleration is positive. A car that is going faster has positiveacceleration. When a car is slowing, the acceleration andvelocity are in opposite directions. The acceleration is negative.

A change in velocity is either a change in an object’s speedor its direction. When a moving object changes direction, itsvelocity changes and it is accelerating. The speed of a horsemoving around on a carousel remains constant, but it isconstantly changing direction. So, the horse is accelerating.

Another example is the motion of Earth around the Sun ina nearly circular path. As a result of its motion, the directionof Earth’s velocity is changing constantly. This means thatEarth is accelerating as it orbits the Sun.

average acceleration (in m/s2) = (final velocity(in m/s2 ) – initial velocity (in m/s2 ))

(final time (s) – initial time (s))

a = (vf – vi)

Calculating AccelerationWhen an object is moving, it may speed up, slow down, or

change direction. Each change in velocity means the object isaccelerating. Even if the acceleration is changing, you can calculate the average acceleration over a period of time. If theobject’s direction does not change, you can use this equationto calculate average acceleration:

In this equation, vi is the starting velocity, and vf is thevelocity at the end. If the object is moving in one direction,then vi is the starting speed, and vf is the final speed. In SIunits acceleration is measured by change in the speed (m/s) ina certain amount of time (s). So acceleration is measured inm/s2, or meters per second squared. Suppose an object has anacceleration of 1 m/s2. This means its velocity increases by 1 m/s each second.

What can a speed-time graph tell you aboutacceleration?

A speed-time graph is used to show the acceleration of anobject moving in one direction. On this type of graph, thevertical axis measures the speed of the object. The horizontalaxis measures the time. The slope of the plotted line showsthe acceleration of the object.

2. Calculate Suppose abird takes off from a treeand flies in a straight line.It reaches a speed of 10 m/s.Calculate the change in thebird’s velocity.

Applying Math

(tf – ti)

1. Apply Give an exampleof positive acceleration andnegative acceleration thatdo not involve anymachines.

8

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 acceleration of an object that is speeding up is always positive.The acceleration of an object that is slowing down is alwaysnegative.

Suppose an airplane is sitting at the end of a runway. Theplane takes off and moves down the runway. It takes 20 s forthe plane to travel from one end of the runway to the other.When the airplane reaches the end of the runway, it is traveling 80 m/s. The airplane is traveling in a straight line.The initial velocity of the plane is 0 m/s and the final velocityof the plane is 80 m/s. The time is 20 seconds. The acceleration for the plane can be calculated as ahown below.

The airplane is speeding up as it goes down the runway.The final speed is greater than the initial speed. The acceleration is a positive number.

3. Explain Why is theacceleration of an objectmoving at a constantvelocity always zero?

Positiveacceleration

TimeSp

eed

4. Relabel the figure usingwords instead of the foursymbols that appear on thefigure.

Picture This

Speed-Time Graph

start takeofftime = tispeed = vi speed = vf

time = tf0 s0 m/s 80 m/s

20 s

Acceleration at Takeoff

9

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 person2 s to come to a stop. The initial velocity is 3 m/s and the finalvelocity is 0 m/s. The total time is 2 seconds. The calculationfor the skateboarder’s acceleration is as follows:

The skateboarder is slowing down. The final speed is lessthan the initial speed. The acceleration is a negative number.

Amusement Park AccelerationRoller coasters are exciting rides. Engineers who design

roller coasters use the laws of physics. The steep drops andloops of steel roller coasters give the rider large accelerations.When riders move down a steep hill, gravity causes them toaccelerate toward the ground. When riders go around a sharpturn, they are also accelerated. When they accelerate during a turn, it feels like a force is pushing them toward the side of the car.

Look at the roller coaster in the figure below. The car of theroller coaster slows down, or has a negative acceleration, as itcreeps up to the top of the hill. Then it speeds up, or has apositive acceleration, as it moves down the hill. Its positiveacceleration is due to gravity.6. Label the place on this

roller coaster where the carwould have greatest acceleration, leastacceleration, and velocity=0.

Picture This

5. Identify Circle the letterof the units that representnegative acceleration.

a. 2 m/sb. 30 m/s2

c. –7 m/sd. –14 m/s2

Time

Spee

d

Negative acceleration

a!! "(v

(f

tf

#- t

v

i)i )

" !"(0 m/s

2#

s3 m/s)"! 1.5 m/s2

10

1. Review the term and its definition in the Mini Glossary. Explain why a change in velocityaffects acceleration.

2. Complete the chart to organize information about how average acceleration is calculated.

3. As you read the section, you made an outline describing the points covered in eachparagraph. How did you decide what to write as the major points in your outline?

Which is greater innegative acceleration,initial or final velocity?

Which is greater inpositive acceleration,

initial or final velocity?

The formula foracceleration:

acceleration: the change in velocity divided by the time forthe change to occur

After You ReadMini Glossary

11

When you throw a football, you apply a force that moves anobject. Think of three more examples from sports in whichforce is used to move something. Write them below.

Before You Read

Read to LearnWhat is force?

When you shoot a basketball or kick a soccer ball, you areexerting a force on an object. A force is a push or pull thatone object exerts on another. Force is a vector, like velocityand acceleration. It has a size and a direction. The size of aforce is its strength. The direction is the direction it is pushedor pulled. The SI unit for force is newtons (N). Lifting a fullcan of soft drink takes about 3 N of force.

How does force change motion?Think about a tennis player hitting a ball. What happens to

the motion of the ball when the racket hits it? The force ofthe racket hitting the ball makes the ball stop. Then the forcemakes the ball move in a different direction.

Balanced Forces Not all forces change velocity. In thefigure on the next page, two students are pushing on oppositesides of a box, if both students push with an equal force, thebox does not move. When two or more forces act on an object at the same time, the forces combine. Net force is thecombination of two or more forces acting on an object at thesame time. When two students push with the same force inopposite directions, the two forces cancel out. The net force iszero. Balanced forces are forces on an object that are equal insize and opposite in direction.

Motion, Acceleration, and Forcessection ! Motion and Forces3

What You’ll Learn" how force and motion

are related" the difference between

static friction and slidingfriction

" how air resistanceaffects falling objects

Create a Quiz As you arereading this section, write fivequestions that could be usedon a quiz. Be sure to include theanswers.

Study Coach

!C Find Main Ideas As youread, use quarter- or half- sheetsof paper to help you identify themain ideas about motion andforces.

Motion

Forces

12

What is the result of unbalanced forces?Not all forces in opposite directions cancel each other. Think

about two students pushing on the opposite sides of a box.What happens if one student pushes harder than the other as inthe first figure below? The box will move in the direction of thelarger force. The student who is pushing harder will move thebox in the direction of the force. The net force that moves thebox is the difference between the two forces. They areunbalanced forces.

Suppose both students push on the same side of the box asin the second figure below. Both students are exerting force inthe same direction. The forces are combined, or addedtogether, because they are exerted on the box in the samedirection. The net force is equal to both forces added together.The forces combine to produce a net force that is not zero.Unbalanced forces exist when the forces acting on an objectproduce a net force that is not zero.

How do unbalanced forces change velocity?Suppose you and another person are pushing on a front

door from opposite sides with the same force. The forces onthe door are balanced, so the door does not move. The netforce is zero. But what happens if you push a little harder?The forces are not balanced any more. The door moves in thedirection you are pushing it. So the door has velocity onlywhen the forces are unbalanced. An object’s velocity changesonly when the forces on it are unbalanced.

Net force ! 0" ! 0

Net force ! " !

2. Draw in the space belowan example showing theresult of unbalanced forceson opposite sides of anobject.

Picture This

Net force ! " !

1. Describe Why are theforces in the figure saidto be balanced?

Picture This

13

FrictionSuppose you give a skateboard a push with your hand. The

skateboard speeds up as you push it and keeps moving. Whathappens to the skateboard’s speed as it moves on a flat, levelsurface? The skateboard slows and then stops. It will not keepmoving forever.

The skateboard’s speed changed because of unbalancedforces. The unbalanced force making it stop is called friction.Friction is the force that opposes the sliding motion of twosurfaces that are in contact.

What causes friction?Friction is a force that one object exerts on another. The

size of frictional force depends on what the surfaces of thoseobjects are like. It depends on the materials the surfaces aremade from and the roughness of the surfaces. Even surfacesthat seem completely smooth, like polished metal, have somebumps. Surfaces stick to each other where these bumps toucheach other. Microwelds form between the surfaces. As the firstfigure below shows, microwelds make the surface sticktogether and cause friction.

What happens to the force between two surfaces when thesurfaces are pushing together increases? As the second figureabove shows, the frictional force increases. This is because moreof the bumps on the surface of the materials come into contactwith each other. The strength of the microwelds increases,causing more friction.

3. Explain how frictionmakes a skateboard slowdown.

4. Label the microwelds inthe diagram on the left.

Picture ThisForce

Moreforce

Surfaces Same twosurfaces

Microwelds form where bumps come into contact.

More force presses the bumps closer together.

Force

Surfaces

Microwelds form where bumps come into contact.

14

What is static friction?Imagine you are trying to push a box along the floor. You

have to break the microwelds that have formed between thesurface of the floor and the surface of the box. Even if youapply a strong force, the box may not move. This means thatthere is an additional force acting against your push. Thisforce is a frictional force called static force that occurs becauseof the microwelds. Static friction is the frictional force thatprevents two surfaces in contact from sliding past each other.

What is sliding friction?Now suppose you and another person are pushing a box,

and it is moving, as in the figure below. The force you areapplying to the box is larger than the force from static friction, so the box is moving. But if you stop pushing thebox, the box will slow down and stop. This is because there isanother type of friction opposing the motion of the box.Sliding friction is the force that acts in the opposite directionto the motion of a surface sliding on another surface. Slidingfriction causes the box to slow down and stop when you stoppushing it. The force of sliding friction is less than the force ofstatic friction.

What is rolling friction?An object can also be slowed down when it is rolling across

a surface. Rolling friction is the frictional force that slows arolling object. Rolling friction has much less of an effect thansliding friction or static friction. When a skateboard that youpush across the sidewalk eventually comes to a stop, it isbecause of rolling friction.

5. Apply In yourexperience, what couldreduce the static frictionthat makes it difficult tomove a box across thefloor?

6. Label the arrows inthe figure with the termsapplied force and sliding friction.

Picture This

15

Air ResistanceIf you drop an apple and a feather, they both fall toward

Earth because of gravity. Gravity pulls all objects downwardwith the same force. But as they fall through the air, the applewill move faster. Why don’t an apple and a feather fall at thesame speed? It is because another force opposes their fall. Airresistance is a frictional force that opposes the movement ofobjects that fall through the air. Without air resistance, allobjects would fall at the same speed. Air resistance causesobjects to accelerate differently.

Imagine that you drop two identical plastic bags at thesame time. One is open, and the other one is crushed into aball. When you drop them, the downward force of gravity onthe bags is the same. But the upward force of air resistance onthe bags is different. The crumpled bag has less air resistanceon it. Therefore, the crumpled bag will fall faster. The airresistance on an object depends on the speed, size, and shapeof the object.

A parachute uses air resistance to slow a person’s fall. As aperson falls through the air, gravity pulls her toward Earth.But with an open parachute, the air resistance of the parachute is greater. This slows the person’s fall.

What is terminal velocity?As an object falls, its velocity increases. If a skydiver fell

without a parachute for 2,000 m and there were no air resistance, the velocity would be almost 200 m/s, or morethan 700 km/h.

As the speed of a falling object increases, the upward forceof air resistance also increases. As a skydiver falls and startsmoving faster, air resistance pushing up also increases. Thenet force on the skydiver decreases during the fall. Eventually,the air resistance equals the downward force of gravity. At thispoint, the net force is zero. So the velocity does not change.The object continues falling at the same speed. This speed iscalled the terminal velocity. Terminal velocity is the highestspeed an object can reach as it is falling.

Like air resistance, the terminal velocity depends on the size,shape, and material of the falling object. The air resistance on anopen parachute is larger than the air resistance on a closed parachute. So the terminal velocity a skydiver reaches whenfalling with an open parachute is slow enough for a safe landing.

8. Re-Phrase How can youexplain terminal velocityto someone in everydaylanguage?

7. Define What is thefrictional force thatopposes the movement ofobjects that fall throughthe air?

16

1. Review the terms and their definitions in the Mini Glossary above. Choose two terms thatare related, and write a sentence using both terms.

2. In the diagram below show one characteristic each of rolling friction, static friction, andsliding friction. In the middle, write two things they have in common.

air resistance: a frictional force that opposes the movementof objects that fall through the air

balanced forces: equal but opposite forces acting on an object

force: a push or pull on an objectfriction: the force that opposes the sliding motion of two

surfaces that are in contact

net force: the combination of forces acting on an objectstatic friction: the frictional force that prevents two surfaces

in contact from sliding past each othersliding friction: the force that acts in the opposite direction

to the motion of a surface sliding on another surfaceunbalanced forces: when the forces acting on an object

produce a net force that is not zero

After You ReadMini Glossary

Sliding: All Three: Static:

Rolling: