Linear Motion

All Motion is Relative This means when we describe motion we do it relative to somethingThis means when we describe motion we do it relative to something The Train is leaving the station or is the station leaving the train?The Train is leaving the station or is the station leaving the train?

All Motion is Relative Even as we stand still –Rotating (30 o 1500 kilometers/h –Revolving around km/h –Galaxy milling 70,000 km/h –Galaxy 792,000 km/h –Galaxy 2.1 million km/h Linear 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 Motion

Linear Speed Speed is a “scalar quantity” Speed is a “scalar quantity” –does not include direction. I am running at 10 mph, but I do not tell you where – this is speed. I am running at 10 mph, but I do not tell you where – this is speed. Speed is my distance covered divided by the time it takes meSpeed is my distance covered divided by the time it takes me

mi/h (mph) – Miles per hourmi/h (mph) – Miles per hour km/h – Kilometers per hourkm/h – Kilometers per hour m/s – Meters per secondm/s – Meters per second Light-years / centuryLight-years / century The symbol / is read as “per”The symbol / is read as “per” Linear Speed

Speed 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 Speed

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

Linear Speed Average Speed Therefore in planning a trip we think about average speedTherefore in planning a trip we think about average speed Average VelocityAverage Velocity –Total distance (d) covered/ time (t) v = d 2 – d 1 v = d 2 – d 1 t

If Downtown is 10 miles and it will take me 30 minutes when my average speed is 20 mi/hIf Downtown is 10 miles and it will take me 30 minutes when my average speed is 20 mi/h This is a lot different from an instantaneous speed of 40 mi/h.This is a lot different from an instantaneous speed of 40 mi/h. If we know our average speed and the time traveled we can arrange the formula to tell us our distance traveled. If we know our average speed and the time traveled we can arrange the formula to tell us our distance traveled. Total distance = Avg speed x timeTotal distance = Avg speed x time d = vt d = vt

Linear Velocity Velocity is a “vector quantity”Velocity is a “vector quantity” –this means is has Speed and Direction If a car travels at of 60 km/h we have defined its speed If a car travels at of 60 km/h we have defined its speed If we say it is traveling at 60km/h heading north we have defined its Velocity!If we say it is traveling at 60km/h heading north we have defined its Velocity!

Going in a straight line at the same speed is called Constant Velocity.Going in a straight line at the same speed is called Constant Velocity. But if we change our speed (brake at a light) or our direction (turn a corner) then we have a Changing VelocityBut if we change our speed (brake at a light) or our direction (turn a corner) then we have a Changing Velocity Changing our speed or direction is Acceleration Changing our speed or direction is Acceleration

Linear Acceleration Acceleration is how quickly velocity changesAcceleration is how quickly velocity changes a = v 2 – v 1 a = v 2 – v 1 t When we accelerate in a car from stop to 60km/h in 5 seconds.When we accelerate in a car from 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 Acceleration We have changed our speed and this is Acceleration.We have changed our speed and this is Acceleration. The same applies when we are in a car that slows – this is called negative acceleration or Deceleration The same applies when we are in a car that slows – this is called negative acceleration or Deceleration When we brake to a stop from 60km/h in 5 seconds.When we brake to a stop from 60km/h in 5 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 in direction.Acceleration also applies to changes in direction. We feel the effects when in a car we are pushed to the side when we turn a sharp cornerWe feel the effects when in a car we are pushed to the side when we turn a sharp corner Acceleration is measured in km/hr/s, but usually m/s 2 in Physics Acceleration is measured in km/hr/s, but usually m/s 2 in Physics

Free Fall – How Fast If a rock is dropped off the side of a cliff we would expect it to fall and during the fall we would expect it to accelerate.If a rock is dropped off the side of a cliff we would expect it to fall and during the fall we would expect it to accelerate. If there was no air resistance its speed would increase by approximately 10m/s every second.If there was no air resistance its speed would increase by approximately 10m/s every second.

After 5 secondsAfter 5 seconds –What would be its speed? –v = at –v = 10 m/s 2 (5 s) = 50 m/s Acceleration due to gravity is referred to as g and is accurately 9.8 m/s 2Acceleration due to gravity is referred to as g and is accurately 9.8 m/s 2 Free Fall – How Fast

TimeVelocity final v Avg y this second Total y 00000

Free Fall If the rock was thrown up into the air we would still see the rate of velocity change as -10m/s 2. 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/s 2.

TimeVelocity final V Avg Y this second Total Y 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? 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? 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? The distance traveled by an object starting at rest and uniformly accelerating is: d= ½ gt 2

TimeVelocity final v Avg y this second Total y 00000

TimeVelocity final V Avg Y this second Total Y V initial = 30 m/s up

Air 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?