Motion, Speed, and Acceleration

Linear MotionLinear Motion--

Motion Along a LineMotion Along a Line

Defining Motion

Speed and VelocitySpeed and Velocity

Consider the Following

Right now, this very instance, are Right now, this very instance, are you moving?you moving?

The Earth in Space

Earth rotates around its axis at: 1,043 mphEarth rotates around its axis at: 1,043 mph Earth revolves around the sun at: 66,660 mphEarth revolves around the sun at: 66,660 mph Solar system moves toward Vega at: 43,200 Solar system moves toward Vega at: 43,200

mph mph Solar system revolves around the Milky Way Solar system revolves around the Milky Way

Galaxy at: 489,600 mph Galaxy at: 489,600 mph The Milky Way Galaxy moves toward The Milky Way Galaxy moves toward

Andromeda at: 180,000 mph Andromeda at: 180,000 mph The Local Group is pulled toward the Local The Local Group is pulled toward the Local

Supercluster at: 540,000 mphSupercluster at: 540,000 mph

What’s it Mean?

Relative to some point in space Relative to some point in space you are moving approximately you are moving approximately 1,320,503 mph or 367 miles 1,320,503 mph or 367 miles

every second!every second!

But, are you moving relative to But, are you moving relative to the classroom?the classroom?

Motion - Definitions

Motion is relative Motion is relative Motion: Occurs when an object Motion: Occurs when an object

changes its position relative to a changes its position relative to a reference point reference point

Distance: How far an object has Distance: How far an object has moved moved

Speed

Speed – the distance an object Speed – the distance an object travels per unit of time travels per unit of time

Speed – a change in distance over Speed – a change in distance over time also called a time also called a raterate

Rate – any change over timeRate – any change over timeSpeed = distance / time s=d/tSpeed = distance / time s=d/t

Types of Speed

Speed that doesn’t change over time is Speed that doesn’t change over time is called constant speedcalled constant speed

Speed is usually not constant in our Speed is usually not constant in our day-to-day lives most objects have a day-to-day lives most objects have a changing speed because of other changing speed because of other forces acting on themforces acting on them

Average speed = total distance / total Average speed = total distance / total time (computed)time (computed)

Instantaneous speed – speed at a Instantaneous speed – speed at a given point in time (measured)given point in time (measured)

Speed vs. Velocity

What is the difference between What is the difference between speed and velocity?speed and velocity?

To answer this we need to To answer this we need to understand “different kinds of understand “different kinds of numbers”numbers”

Numbers – Two types

ScalarsScalarsCommon numbers we use everydayCommon numbers we use everydayScalars give us an amountScalars give us an amount

VectorsVectorsLike scalars they show an amountLike scalars they show an amountUnlike scalars they show directionUnlike scalars they show direction

Speed with Direction

Velocity is speed with direction Velocity is speed with direction What type of “number” do we call What type of “number” do we call

velocity?velocity?Velocity can be fast or slow just like Velocity can be fast or slow just like

speed only a direction is addedspeed only a direction is addedMovement to the right or up is Movement to the right or up is

positive and left or down is negativepositive and left or down is negative

Distance vs. Displacement

Distance – how far an object has Distance – how far an object has movedmoved

Displacement – distance and Displacement – distance and direction from a starting pointdirection from a starting point

Questions

Can you have a negative speed?Can you have a negative speed?Can you have a negative velocity?Can you have a negative velocity? Is distance a vector or a scalar?Is distance a vector or a scalar?How about displacement?How about displacement?What is the relationship between What is the relationship between

distance and displacement?distance and displacement?

Acceleration

Changing VelocityChanging Velocity

Acceleration

When an object changes When an object changes speedspeed or or directiondirection, it is acceleration – this is , it is acceleration – this is an important point!an important point!

Why is going around a curve at the Why is going around a curve at the same speed acceleration?same speed acceleration?

Calculating Acceleration

Acceleration = change in velocity Acceleration = change in velocity /time/time

Change in velocity = final velocity – Change in velocity = final velocity – initial velocityinitial velocity

VF-VI

TF-TI

VF-VI

Δt

Acceleration

Do the math – units of acceleration Do the math – units of acceleration are in meters per second per are in meters per second per second or meters per second second or meters per second squared – m/ssquared – m/s22

Showing Motion

Distance, Velocity and Distance, Velocity and Acceleration GraphsAcceleration Graphs

Showing Motion

Distance – time graph displays the Distance – time graph displays the motion of an object over timemotion of an object over time

Distance is the dependant variableDistance is the dependant variableDistance goes on the vertical axisDistance goes on the vertical axisTime is the independent variable so Time is the independent variable so

it is placed on the horizontal axisit is placed on the horizontal axis

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Key Points

Make sure you are working with a Make sure you are working with a Distance/Time GraphDistance/Time Graph

Distance is the y axis or riseDistance is the y axis or riseTime is the x axis or runTime is the x axis or runSlope = rise/run or distance/time Slope = rise/run or distance/time

therefore, slope = velocitytherefore, slope = velocity ““+” slope = moving right, “-” slope = +” slope = moving right, “-” slope =

moving leftmoving left

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Velocity vs. Time

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Question

What does the slope of a What does the slope of a velocity/time graph represent?velocity/time graph represent?

What does the area under a What does the area under a velocity/time graph represent?velocity/time graph represent?

d=vit + ½at2

Key Points

Make sure you are working with a Make sure you are working with a velocity/time graphvelocity/time graph

Slope = rise/run or velocity/time Slope = rise/run or velocity/time therefore, Slope = accelerationtherefore, Slope = acceleration

““+” slope = accelerating right, “-” slope +” slope = accelerating right, “-” slope = accelerating left = accelerating left

Acceleration units are m/sAcceleration units are m/s22

Area under graph is the distance Area under graph is the distance traveledtraveled

Freefall

All objects near earth’s surface All objects near earth’s surface accelerate downward at 9.8 m/saccelerate downward at 9.8 m/s22

Known as gKnown as gIgnores air resistanceIgnores air resistanceALLALL objects accelerate at the objects accelerate at the

same ratesame rate

v=gt and d=½gt2