Glencoe Chapter 3

Describing Motion

Who Wins?????

Racer with the fastest speed?Racer with the shortest elapsed time?What is motion?What is speed?How is speed different from velocity?

Battery Buggy

After watching the buggy, how is it’s motion different/similar to a 100 meter sprinter? What if the batteries were close to dead?

Motion is Relative Perception of motion by

humans is always related to nearby objects.

Even if there is motion, but no nearby reference, motion is not perceived by humans.

3.1 Picturing Motion

When an object moves, it’s position changes.

A MOTION DIAGRAM is a tool that may be used to study the motion of an object.

How do you know the answer is correct?

Motion Diagrams—you draw!

What kind of motion does the diagram depict?

Operational Definition An Operational Definition defines a

concept in terms of the procedure or operation used.

Examples Rest? Object does not change position with

relation to a reference point. Constant speed? Object travels equal

distances in equal time periods. Acceleration? Deceleration

What’s Happening here?

Or here?

Particle Model

These types of Diagrams are a little difficult to draw. Maybe we can substitute something else for little pictures of the moving object…

A ticker-tape timer

 

Ticker Tape: "slower" acceleration

**  *    *       *           *                 *                       *                               *                                     

   

Ticker Tape: "Faster" acceleration

**   *        *               *                        *                                   *                               

 

Ticker Tape: "slower" deceleration

            *                                   *                        *               *         *   **

   

Ticker Tape: "faster" deceleration

           *                              *                   *           *      *   * *                        

Ticker-tape Math

Speed = distancetime

From timer device rate

Time Taken = 5 X .025s = 0.125 s

Now you try it….

Page 46 of your text, #1-4

3.2 Where and When?

Coordinate Systems—Tell where zero point of variable you are studying is and the direction in which the value of the variable increases.

Origin—Point at which values for variable are zero.

X-Y Coordinate System Motion of many types may be shown on a

coordinate system, for example a ball thrown upward A cannon firing a cannonball a high diver diving off a board A high jumper

We can use an x-y system, X is horizontal movement Y is vertical movement

We can define upward as positive, which is standard.

We can define to the right as positiveHowever, you can choose any

direction as either positive or negative, just make sure the opposite direction has an opposite sign.

Symbols in Physics

Symbols are frequently used to represent quantities in Physicsm represents mass SI unit kgt represents time ss represents speed m/s d represents distance ma represents acceleration m/s2

v represents velocity m/sΔd represents displacement m

Vectors and Scalars Another way of representing the position of an

object would be to use a vector. Vectors or scalars are used to represent quantitiesrepresent quantities in physics.

A scalar is a line segment, whose length represents only magnitude Time is a scalar quantity

A Time interval is the difference between two time periods i.e 2 hours interval between 2:00 and 4:00

Mass is a scalar quantity, along with others

Vectors

A vector is a ray whose length represents magnitude, and the ray points in the direction.

Vectors are used to represent quantities that have both magnitude as well as direction. Displacement is a vector quantity

Is the distance and direction between two positions

ExamplesExamples

Speed……….. Velocity……... Acceleration.. Time…………. Distance……. Force………

Scalar quantity

Vector quantity

Vector

scalar

scalar

vector

Vector Quantities

Vector quantities are represented with arrows over the symbol. Velocity

acceleration

ExamplesEquation for acceleration

A position vector drawn from origin to position of object

x

y

d0

Position Vectors

Another Position vector

Velocity Vectors

Displacement vs. Position

Position is the position where an object is located. Indicated as “d”, or sometimes d0, d1

Displacement is the change in position of an object between two time periods. Indicated as “Δd”

Found by subtracting, d1- d0

Δd = d1-d0

Time Interval

Time intervals (Δt) are defined as the time between two time periods.

Δt = t1-t0

Displacement vectors drawn between positions at two different time periodsDisplacement (Δd) is equal to difference between two position vectors (d1-d0) Δd = d1-d0

Velocity vectors drawn for each time period, length indicates magnitude (speed)

Distance vs. Displacement

You drive the path, and your odometer goes up by 8 miles (your distance).

Your displacement is the shorter directed distance from start to stop (purple arrow).

What if you drove in a circle?

start

stop

3.3 Velocity and Acceleration

Motion diagrams can be used to show objects moving with different speeds and different kinds of motion.

Motion diagrams can show position and time, but can we combine them to determine a rate of motion?

3.3 Velocity and Acceleration

interval timentdisplaceme Velocity

** Speed and velocity are similar except ** Speed and velocity are similar except speed is scalar and velocity vector.speed is scalar and velocity vector.

Velocity = {speed with a direction}

Examples:

70 mph is a speed.

70 mph North is a velocity.

VelocityVelocity

instantaneous velocity - the velocity that something has at any one instance (The terms instantaneous speed and avg.

speed may also be used)

interval timentdisplaceme = velocity average

t

dv

_

The average velocity for a trip might be 53

miles/hour.

However, during this trip your instantaneous speed

might have been 0 miles/hour at a stoplight

or 70 miles/hour on the open road.

Instantaneous Velocity

Average Velocity, because it is calculated for a time interval, can actually not be calculated for a particular time period

Instantaneous Velocity—velocity at a particular time period. Generally, however, when used in this text, the term “velocity” refers to an Instantaneous Velocity.

Displacement from Velocity

tvd

Final Position : This equation can be used to find “where” an object will be at some time period.

01 ddd tvd tvdd 01

Substitute Into

To get

Then rearrange to get

tvdd 01

Acceleration - rate of change in velocity due to change in speed or direction

AccelerationAcceleration

interval time velocityof change =on Accelerati

Example:9.8 meters/second2 downward

t

vv

t

va

01

Positive vs. Negative

Is it possible to have a negative velocity and a positive acceleration?

Is it possible to have a positive velocity and a negative acceleration?

Is it possible to have a positive velocity and a positive acceleration?

Is it possible to have a negative velocity and a negative acceleration?

Velocity & Acceleration Sign Chart

V E L O C I T YACCELERATION

+ -

+Moving forward;

Speeding up

Moving backward;

Slowing down

- Moving forward;

Slowing down

Moving backward;

Speeding up

End of Chapter 3

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