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Velocity and

Acceleration

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1. Frame of Reference

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Frame of Reference – how you determine the position. We normally use N-S-E-W.

Our Reference: Positive, (+) Moving RIGHT or Moving UP Negative, (-) Moving LEFT or Moving DOWN If you are not sure of the direction, use Positive(+)Choose your starting position as Zero (0), unless

the problem tells you otherwise!

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Scalar Quantity - Magnitude - “How much”Direction does not matterMass, temperature, and time are scalar

quantities

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Vector Quantity –Magnitude AND DirectionHow much and which wayVelocity, force and

displacement are vector quantities.

Use “vector diagrams” to represent these quantities.

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The arrow shows the directionLength of arrow is proportional to the magnitude.High velocity to the right Low velocity to the left

Position – your location using the frame of reference. Ships use longitude and latitude. Symbol is d for horizontal motion. (your book

uses x)Vector quantity – magnitude and direction. I am located 5 km south of home.

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Displacement – change in position“How far out of place an object is”Symbol is d (x-horizontal, y-vertical) “delta” is “change in” d = df - di

Vector Quantity: Magnitude and DirectionUnits include m (meter), km, cm, mmYou travel 10 km EastDisplacement = zero (0) when you return to

the original position. You are not “out of place”

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You travel 10 km East, stop and then turn around and travel 10 km West. Displacement, d = 0 10 km East 10 km West Displacement = d = 0

You travel 10 km East, stop and then turn around and travel 15 km West. 10 km East

15 km West Displacement = d = -5km

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Distance How far you traveledScalar quantityMagnitude only I drove 20 km today.10 km East 10 km West Distance Traveled = 20 km10 km East 15 km West Distance Traveled = 25 km

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TimeClock readingScalar QuantitySymbol is tUnits include seconds, minutes, hours, days

Time IntervalElapsed time, change in timeSymbol tScalar Quantityt = tf – ti (final time – initial time)Units include seconds, minutes, hours, days

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2. Velocity Motion – Change in position Average Velocity

Rate of change in position =

IntervalTimeTotalntDisplacemeTotal

TimeinChangePositioninChangev

hrkm

sm

tdv

v

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Vector Quantity – Magnitude and Direction We will use positive (+) and negative (-) to show

direction + right or up - left or down + moving towards you (you are the reference) - moving away from you Average velocity does not indicate what happens

during the time interval. You could have stopped, sped up, or even slowed down.

vvv

v

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Instantaneous velocity – the velocity at any given instant in time.

Constant velocity - all the instantaneous velocities are equal. “Cruise Control”

Only true judgment of velocity is a reference point that is not moving.

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Overall Velocity Moving Sidewalk +3m/s You walk on it +1 m/s Overall velocity +4m/sMoving sidewalk +3m/s You walk backwards -1m/s Overall velocity +2m/s

Speed – scalar quantity, distance traveled over a period of time. No indication of direction!

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3. Acceleration Average Acceleration

Rate of change in velocity

Toughest time to walk on the bus? When it is speeding up or slowing down!

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Average acceleration =

vf = final velocity

vi = initial velocity

Units :

NOT!!

IntervalTimeVelocityinChange

tvv

tva if

tva

2sm

ssm

a

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Vector Quantity – magnitude and direction If you are moving right or up and

Speeding Up : +a (positive acceleration) Slowing Down : -a (negative acceleration) This is normal conditions!

If you are moving left or down and Speeding Up : -a (negative acceleration) Slowing Down : +a (positive acceleration)

If you do not know direction left or right use Speeding Up : +a Slowing Down : -a

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Just remember :The direction of the acceleration vector

depends on : Whether the object is speeding up

or slowing down. Whether the object is moving in the

positive (+) or negative (-) direction.Rule of Thumb –

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

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If you are moving from rest vi = 0 (zero)

If you are coming to a stop vf = 0 (zero)

If you are moving at constant velocity = 0 (cruise control)

If you are not moving : v = 0 Acceleration is not discussed! (aka a 0)

a