Linear MotionLinear Motion

Linear MotionLinear MotionAll Motion is RelativeAll Motion is Relative

• This means when we describe motion This means when we describe motion we do it relative to something we do it relative to something

• The Train is leaving the station or is The Train is leaving the station or is the station leaving the train? the station leaving the train?

All Motion is Relative

• Even as we stand still – Rotating (30o N) @ 1500 kilometers/h– Revolving around sun @107,000 km/h – Galaxy milling around @ 70,000 km/h– Galaxy revolving @ 792,000 km/h– Galaxy outward @ 2.1 million km/h

Linear MotionLinear Motion

• A car in the Indy 500 ends up at the same point.

• On the school bus traveling at 30mph you throw a ball to a classmate, how fast is the ball moving?

• We usually describe motion relative to the surface of the earth

Linear MotionLinear Motion

Linear SpeedLinear Speed• Speed Speed is a “scalar quantity” is a “scalar quantity”

– does not include direction.does not include direction.

• I am running at 10 mph, but I do I am running at 10 mph, but I do not tell you where – this is speed.not tell you where – this is speed.

• Speed is my distance covered Speed is my distance covered divided by the time it takes medivided by the time it takes me

• mi/h (mph) – Miles per hour mi/h (mph) – Miles per hour

• km/h – Kilometers per hourkm/h – Kilometers per hour

• m/s – Meters per second m/s – Meters per second

• Light-years / centuryLight-years / century

• The symbol / is read as “per”The symbol / is read as “per”

Linear SpeedLinear Speed

Linear SpeedLinear SpeedSpeed

• Measure of how fast something moves• Unit of distance divided by unit of time • Two types of measurement

– Instantaneous speed– Average Speed

Instantaneous Speed• You are in a car heading downtown, as

you can see from the speedometer your speed is 40 mi/h.

• Downtown is 10 miles away at this speed, how long will it take you?

• IS THIS TRUE???

Linear SpeedLinear Speed

Linear SpeedLinear SpeedAverage SpeedAverage Speed

• It would take us a lot longer than 15 It would take us a lot longer than 15 minutes to drive downtown because of minutes to drive downtown because of the traffic where we have to slow, stop, the traffic where we have to slow, stop, start, accelerate, slow, stop, etc., etc,.start, accelerate, slow, stop, etc., etc,.

Linear SpeedLinear SpeedAverage SpeedAverage Speed• Therefore in planning a trip we think Therefore in planning a trip we think

about average speedabout average speed• Average VelocityAverage Velocity

– Total distance (d) covered/ time (t)Total distance (d) covered/ time (t)

v = v = dd22 – d – d11

tt

• If Downtown is 10 miles and If Downtown is 10 miles and it will take me 30 minutes when it will take me 30 minutes when my average speed is 20 mi/h my average speed is 20 mi/h

• This is a lot different from an instantaneous This is a lot different from an instantaneous speed of 40 mi/h.speed of 40 mi/h.

• If we know our average speed and the time If we know our average speed and the time traveled we can arrange the formula to tell us traveled we can arrange the formula to tell us our distance traveled.our distance traveled.

• Total distance = Avg speed x timeTotal distance = Avg speed x time

d = vtd = vt

Linear VelocityLinear Velocity• Velocity Velocity is a “vector quantity” is a “vector quantity”

– this means is has Speed and Directionthis means is has Speed and Direction

• If a car travels at of 60 km/h we have If a car travels at of 60 km/h we have defined its speeddefined its speed

• If we say it is traveling at 60km/h If we say it is traveling at 60km/h heading north we have defined its heading north we have defined its VelocityVelocity!!

• Going in a straight line at the same Going in a straight line at the same speed is called speed is called Constant Velocity.Constant Velocity.

• But if we change our speed (brake at But if we change our speed (brake at a light) or our direction (turn a a light) or our direction (turn a corner) then we have a corner) then we have a Changing Changing VelocityVelocity

• Changing our speed or direction is Changing our speed or direction is AccelerationAcceleration

Linear AccelerationLinear Acceleration• Acceleration Acceleration is how quickly velocity is how quickly velocity

changeschanges a = a = vv22 – v – v1 1

tt

• When we accelerate in a car from When we accelerate in a car from stop to 60km/h in 5 seconds.stop to 60km/h in 5 seconds.

a = (60 km/h – 0 km/h)/5s a = (60 km/h – 0 km/h)/5s = 12 km/h/s= 12 km/h/s

Linear AccelerationLinear Acceleration• We have changed our speed and this is We have changed our speed and this is

AccelerationAcceleration..• The same applies when we are in a car that The same applies when we are in a car that

slows – this is called slows – this is called negative acceleration negative acceleration or or DecelerationDeceleration

• When we brake to a stop from 60km/h in 5 When we brake to a stop from 60km/h in 5 seconds.seconds.

a = (0 km/h – 60 km/h)/5s a = (0 km/h – 60 km/h)/5s = – 12 km/h/s= – 12 km/h/s

• Acceleration also applies to changes Acceleration also applies to changes in direction. in direction.

• We feel the effects when in a car we We feel the effects when in a car we are pushed to the side when we turn are pushed to the side when we turn a sharp cornera sharp corner

• Acceleration is measured in km/hr/s, Acceleration is measured in km/hr/s, but but usually m/susually m/s22 in Physics in Physics

Free Fall – How Fast Free Fall – How Fast • If a rock is dropped off the side If a rock is dropped off the side

of a cliff we would expect it to of a cliff we would expect it to fall and during the fall we would fall and during the fall we would expect it to accelerate.expect it to accelerate.

• If there was no air resistance its If there was no air resistance its speed would increase by approximately speed would increase by approximately 10m/s every second.10m/s every second.

• After 5 secondsAfter 5 seconds– What would be its speed?What would be its speed?– v = atv = at– v = 10 m/sv = 10 m/s22 (5 s) = 50 m/s (5 s) = 50 m/s

• Acceleration due to gravity is referred to Acceleration due to gravity is referred to as g and is accurately 9.8 m/sas g and is accurately 9.8 m/s22

Free Fall – How FastFree Fall – How Fast

Time Velocity

final

vAvg y this second

Total y

0 0 0 0 0

Free FallFree Fall• If the rock was thrown up into the air we

would still see the rate of velocity change as -10m/s2.

• But for the first few seconds it would be decelerating, then stopped for a fraction of a second, before it started its acceleration toward the ground at 10m/s2.

Time Velocity

final

VAvg Y this second

Total Y

0 30 30 0 0

V initial = 30 m/s up

Apollo 15 commander

David R. Scott confirmed Galileo's

hypothesis that in the absence

of air resistance all objects fall with the same

velocity.

Free Fall – How Far?Free Fall – How Far?• But there is air resistance on earth.• So???• Would you rather jump out of a plane

with or without a parachute?• Why?

Free Fall – How Far?Free Fall – How Far?• At the end of the first second of something

falling is has a instantaneous speed of 10m/s.

• But this does not mean it has fallen 10m in the first second

• This is where the difference between average speed and instantaneous speed comes in

• It started at zero, so we know the average speed is somewhere between 0 and 10m/s

Free Fall – How Far?Free Fall – How Far?• The distance traveled by an object

starting at rest and uniformly accelerating is:

d= ½ gt2

Time Velocity

final

vAvg y this second

Total y

0 0 0 0 0

Time Velocity

final

VAvg Y this second

Total Y

0 30 30 0 0

V initial = 30 m/s up

Air ResistanceAir Resistance• As we said before in a

vacuum a stone and a feather will fall at the same rate.

• But we know here on Earth that does not happen

• If you were jumping out of a plane, what shape would you like your parachute to be?

Why?