Section 11.1 Distance and Displacement

How fast is the butterfly moving? What direction is it moving?

To describe motion, you must state the _______________________ the object is moving as well as how

_____________ the object is moving. You must also tell its location at a certain time.

What is needed to describe motion completely?

A __________________ of ________________________ 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.

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 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 ________________________________ by.

• When the people on the ______________________ look at one another, they don’t

seem to be moving at all.

To someone riding on a speeding train, others on the train don’t seem to be

________________________.

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 _____________________________.

• 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 _____________________________ to the train.

• Choosing a meaningful frame of reference allows you to describe _______________________ in

a clear and relevant manner.

How are distance and displacement different?

__________________________ 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 _________________________ (m).

• For very large distances, it is more common to make measurements in

___________________________ (km).

• Distances that are smaller than a meter are measured in _____________________ (cm).

To describe an object’s position relative to a given point, you need to know how _____________ away

and in what _________________________ the object is from that point. _______________________

provides this information.

Think about the motion of a roller coaster car.

• The _______________________ of the path along which the car has traveled is

distance.

• ___________________________- 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

__________________.

How do you add displacements?

A _________________________ is a quantity that has magnitude and direction.

Add displacements using vector __________________________.

Displacement is an example of a vector.

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

• __________________________ on a graph or map are used to represent vectors. The

_____________________ of the arrow shows the magnitude of the vector.

• Vector _____________________________ is the combining of vector magnitudes and

directions.

Displacement Along a Straight Line

When two displacements, represented by two vectors, have the same

____________________________, you can add their magnitudes.

If two displacements are in opposite directions, the magnitudes ___________________________ from

each other.

A. _____________ the magnitudes of two displacement vectors that have the same direction.

B. Two displacement vectors with __________________________ 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

___________________________.

Measuring the ____________________________ 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.

The boy walked a total distance of ______ blocks. This is the sum of the magnitudes of each vector along

the path.

The vector in red is called the __________________________ vector, which is the vector sum of two or

more vectors.

The resultant vector points directly from the ___________________ point to the ___________________

point.

Section 11.2 Speed and Velocity

Introduction

The speed of an in-line skater is usually described in _____________________ per

___________________. The speed of a car is usually described in kilometers per hour.

How are ____________________________ speed and _______________________ speed different?

Average speed is computed for the __________________________ duration of a trip, and instantaneous

speed is measured at a particular _____________________________.

______________________ is the ratio of the distance an object moves to the amount of time the object

moves.

The SI unit of speed is _________________ per _______________________ (m/s).

Two ways to express the speed of an object are average speed and instantaneous speed.

Average Speed

Sometimes it is useful to know how fast something moves for an entire trip, even though its speed may

__________________ during the trip.

__________________________ speed, is the total distance traveled, d, divided by the time, t, it takes to

travel that distance.

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?

Read and Understand

What information are you given?

Total Distance (d) = _______ km + ________ km = ___________ km

Total Time (t) = _______ h + ________ h = _________ h

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.

Look Back and Check

Is your answer reasonable?

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?

2. A train travels 190 kilometers in 3.0 hours, and then 120 kilometers in 2.0 hours. What is its

average speed?

Instantaneous Speed

Sometimes you need to know how fast you are going at a particular __________________________.

______________________________ speed, v, is the rate at which an object is moving at a given

moment in time.

The _____________________________ in a car measures the car’s instantaneous speed.

Note the scale markings are given both in km/h and miles per hour, mph.

How can you find the speed from a ______________________-_________________ graph?

The ____________________ of a line on a distance-time graph is speed.

A distance-time graph is a good way to describe ______________________.

Slope is the change in the _____________________ axis value divided by the change in the horizontal

axis value.

A steeper slope on a distance-time graph indicates a ______________________- speed.

How are speed and velocity different?

Velocity is a description of both speed and __________________________ of motion.

_____________________ is a vector.

Sometimes knowing only the speed of an object isn’t enough. You also need to know the

______________________ of the object’s motion.

Together, the speed and direction in which an object is moving are called

_________________________.

A cheetah’s speed may be as fast as 90 km/h. To describe the cheetah’s velocity, you must also know

the _____________________________ in which it is moving.

Vectors can be used to show ____________________ in motion.

• Vectors of varying lengths, each vector corresponding to the velocity at a particular

instant, can represent motion.

• A _____________________ vector represents a faster speed, and a shorter one a slower

speed.

• Vectors point in different directions to represent direction at any moment.

As the sailboat’s direction changes, its velocity also changes, even if its speed stays the

________________.

How do velocities add?

Two or more velocities add by vector _________________________-.

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 __________________________.

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.

11.3 Acceleration

Introduction

The basketball constantly changes ____________________ as it rises and falls. Describing changes in

velocity, and how fast they occur, is a part of describing motion.

How are changes in velocity described?

The rate at which velocity changes is called _________________________________.

Changes in Speed

• In science, acceleration applies to any ____________________ in an object’s velocity.

• Acceleration can be caused by positive (________________________) change in speed or by

negative (____________________________) change in speed.

• __________________________ is an acceleration that slows an object’s speed.

Free fall is the movement of an object toward Earth solely because of _________________________.

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 (____________).

Objects falling near Earth’s surface accelerate downward at a rate of ________ m/s2.

Each second an object is in free fall, its velocity _____________________ downward by 9.8 meters per

second.

The change in the stone’s speed is 9.8 m/s2, the __________________________ due to gravity.

Changes in Direction

Acceleration can be the result of a change in ______________________ at ___________________

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 _____________ time.

Passengers in a car moving along a ____________________ 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 ________________________ and because its _____________________ is decreasing.

A ________________ _______________________ 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 ________________ when the

object is experiencing constant acceleration.

• Constant acceleration is a ___________________ change in velocity.

• An airplane’s acceleration may be constant during a portion of its takeoff.

Constant acceleration during takeoff results in changes to an aircraft’s velocity that is in a constant

________________________.

How can you calculate acceleration?

You can calculate acceleration for _____________________-______________ motion by dividing the

change in velocity by the total time.

Acceleration is the rate at which velocity ___________________. Vi is the initial velocity, vf is the final

velocity, and t is total time.

If the velocity increases, the acceleration is ____________________________. If the velocity decreases,

the acceleration is _________________________.

• If you are coasting downhill on a bicycle, your velocity ______________________, and

your acceleration is positive.

• If you continue coasting on level ground, your velocity ___________________________,

and your acceleration is negative.

Acceleration and velocity are both ______________________________ quantities.

• To determine a change in velocity, ______________________ one velocity vector from

another.

• If the motion is in a ______________________ line, velocity can be treated as speed,

and acceleration is the change in _______________________ divided by the time.

Calculating Acceleration

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?

Read and Understand

What information are you given?

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.

Look Back and Check

Is your answer reasonable?

Objects in free fall accelerate at a rate of ________ m/s2. The ramp is not very _____________. An

acceleration of 3 m/s2 seems reasonable.

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?

Answer:

2. 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:

3. 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:

4. 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:

(The minus sign indicates that the velocity is in the direction ____________________ the acceleration.)

How does a speed-time graph indicate acceleration?

The __________________ of a speed-time graph is acceleration.

You can use a graph to calculate acceleration. Graph speed on the ___________________________ axis

and ________________ on the horizontal axis.

The slope is change in speed divided by change in time, which is equal to the

______________________________.

The skier’s acceleration is positive. The acceleration is 4 m/s2.

Speed-Time Graphs

Constant acceleration is represented on a speed–time graph by a ___________________ line. The slope

of the line is the acceleration.

The graph is an example of a____________________ graph, in which the displayed data form straight-

line parts.

Constant negative acceleration __________________________ speed.

• On a speed-time graph of a bicycle slowing to a stop, a line sloping

___________________________ represents the bicycle decelerating.

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

_____________________________.

The biker moves at a constant speed and then slows to a ___________________.

Distance-Time Graphs

Accelerated motion is represented by a _______________________ line on a distance-time graph.

In a __________________________ graph, a curve connects the data points that are plotted.

A distance-time graph of _______________________________ 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 ___________________ means that the ____________________ is increasing.

What is instantaneous acceleration?

Instantaneous acceleration is how fast a velocity is changing at a specific ________________________.

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 _____________________________.

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

• For an object that is standing still, the acceleration vector is ____________________.