Linear

Motion

Physics

Linear Motion

Linear Motion refers to “motion in a line”. The motion of an object can be described using a number of different quantities.

Time – How long an object is in motion for. In physics, we usually use seconds but in every day life we use minutes, hours, years, etc.

Distance – how far something travels along its path. Can be measured in a wide variety of measurements including kilometers, meters, inches, feet, etc.

Let’s do a Frayer model for

linear motion:

Definition:

How to remember:

Drawing:

Motion in a straight

line

linear motion

vertical horizontal

What it’s NOT:

Speed, velocity, acceleration

Speed - How fast you’re going15 km/hr, 22 cm/s , 2000 mi/hr

Velocity – how fast you’re going in a certain direction

Acceleration - how fast your velocity is changing (speeding up or slowing down)

Example word problem:A soccer ball is moving horizontally at a speed of 3.0

m/s. It then undergoes a constant negative acceleration. After 4.0 s, the ball is moving at 1.5 m/s.

●Instantaneous Speed is the speed at any

specific instance or moment in timeoEx. On a speedometer reading…

you are traveling 35 mph (mi/hr)

or 50 km/h or 25 m/s

●Average Speed is the total distance covered

divided by total time

Types of Speed

How do you calculate average

speed?●The average speed of an object is defined as the total

distance traveled divided by the total time elapsed

Average Speed = total distance total time

Speed = d t Michael Phelps can swim a 200 m

butterfly race in 1:52.09. What would be his average speed?

Speed, cont

Speed is a scalar quantity, meaning it has no

direction. Other examples include distance and time.

Example:

speed: I was going 75 mi/hr

mass: I weigh 75 kilograms

time: there are 45 minutes left of class

Vector

Some quantities are vectors, meaning a number with a unit and direction

Common vectors that we deal with in physics include

displacement, velocity, and acceleration.

Pictorial Representation

●An arrow represents a vector

oLength = magnitude (size) of vector

oDirection = direction of vector

Pictorial Representation

●This arrow could represent a vector of

magnitude 10 point to the “right”

●This arrow could represent a vector of

magnitude 5 point to the “left”

Practice!

●Draw an empty Venn Diagram like this

Scalar Vector

Label one side scalar, other

vector

●Magnitude

●Size

●Direction

●Units

●Distance

●Displacement

●Speed

●velocity

●Acceleration

●Mass

●Weight

●12 cm

●47 kg (mass)

●470 Newtons (weight)

●50 meters

●50 meters West

●25 m/s

●25 m/s toward home

●25 m/s away from home

●10 m/s2

●10 m/s2 toward the ground

Place these words in the correct space on the diagram:

Displacement vs. distance:

1. Displacement: how far its position is from the starting point

(in meters with a direction). A measurement of how far you

“displaced” meaning changed your position. Remember,

displacement is a vector so you need a direction!

Example:

I can jump 4 feet, up.

oDistance: how far an object travels (in meters)

Displacement Isn’t Distance

●The displacement of an object is not the same

as the distance it travelsoExample: Throw a ball straight up and then catch

it at the same point you released it The distance is twice the height

The displacement is zero

Distance & Displacement

Distance & Displacement

B

A

C

5 m

4 m

3 m

Your distance traveled is 7m

You walk from A to B to C.

What is your distance traveled?

What is your displacement from A?

Your displacement form A is 5 m

Horizontal Displacement

• When displacement is horizontally oriented, we refer to an “imaginary line”.

• Any displacement to the right (or forward) of the line, we have a positive displacement.

• Any displacement to the left (backwards) of the line, we experience a negative displacement.

Vertical Displacement• Just as we do with horizontal displacement, we refer to an

imaginary y-axis.

• Moving up the line will be a positive displacement, and moving down the line will be a negative displacement.

Let’s do Frayers for distance &

displacement:

Definition:

Don’t confuse this with:How to remember:

Drawing:

Velocity

●The average velocity of an object is defined

as the total displacement traveled divided by

the total time elapsed

●Velocity is a vector quantity

Average Velocity = total displacement total time

V = x t

Velocity

●It takes time for an object to undergo a displacement

●The average velocity is rate at which the displacement occurs

●generally use a time interval, so let ti = 0

V (average) = Δx = Xfinal – Xinitiative = xf - xi Δt tfinal –tinitiative t

Velocity, cont.

●Pull back car example and demonstration

Speed vs. Velocity

●Cars on both paths have the same average velocity

since they had the same displacement in the same time

interval

●The car on the blue path will have a greater average

speed since the distance it traveled is larger

Let’s do Frayers for speed &

velocity

Definition:

Don’t confuse this with:How to remember:

How to calculate:

Speed vs. Velocity

●You drive from Yakima to Seattle (140 miles away)

●You stop in Ellensburg for a 2 hr lunch with a friend.

●Your total driving time is 2 hours

●What is the average speed?

●What is the average velocity?

●Remember,

speed = total distance/ total time

Concept Map: Linear Motion

The position

changing

How quickly the

position changes

called

called

which is

calculated by

which is

calculated by

which is

calculated by

which is

calculated by

Adding all legs

of the journey

distance

displacemen

t

speed

velocit

y

Xfinal –x initial

Total distance

Total time

xfinal –x initial

time

Acceleration●Acceleration is a measure of how quickly

velocity is changing.

●Change in velocity divided by the change in time

TIME 0.00 sec 1.00 sec 2.00 sec 3.00 sec 4.00 sec

VELOCITY 0 mi/hr 10 mi/hr 20 mi/hr 30 mi/hi 40 mi/hr

Acceleration

Great animation showing acceleration:http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm ●Changing velocity (not constant) means an

acceleration is present

●Units: m/s2 (SI) other examples: cm/s2 ft/s2

Relationship Between Velocity &

Acceleration

●Uniform velocity (shown by red arrows maintaining

the same size)

●Acceleration equals zero

Relationship Between Velocity &

Acceleration

●Velocity and acceleration are in the same direction

●Acceleration is uniform (blue arrows maintain the

same length)

●Velocity is increasing (red arrows are getting longer)

●Positive velocity and positive acceleration

Relationship Between Velocity &

Acceleration

●Acceleration and velocity are in opposite directions

●Acceleration is uniform (blue arrows maintain the

same length)

●Velocity is decreasing (red arrows are getting shorter)

●Velocity is positive and acceleration is negative

Acceleration

Sometimes we are given acceleration and want to know the velocity of an object after a certain amount of time passes. We can figure the velocity out by simply rearranging the equation:

To look more like:

Velocityfinal = Velocityinitial + at

Let’s do a Frayer for acceleration :

Definition:

Don’t confuse this with:How to remember:

How to calculate:

Acceleration Example 1

A bird is flying at a speed of 35.8 m/s. If it

takes 2.0 s to come to a complete stop,

what acceleration would it have?

Example 2

I can run at a speed of 25 m/s and accelerate at 3.0 m/s/s for 5 seconds. How fast would I be running after 5 seconds?

Acceleration Example 3

●A car is said to go "zero to sixty in six

point seven seconds". What is its

acceleration in m/s2?

Acceleration example 4

A toy traveling at 50 cm/s and slows down to 20 cm/s in 10 seconds. What is the toy’s acceleration?

Concept Map: Linear Motion

The position

changing

How quickly the

position changes

The rate at which the

movement changes

called

called

which is

calculated by

which is

calculated by

which is

calculated by

which is

calculated by

which is

calculated by

Adding all legs

of the journeydistance

displacemen

t

speed

velocit

y

acceleratio

n

Xfinal –x initial

Total distance

Total time

xfinal –x initial

time

vfinal –v initial

time

called