# Unit 2 Linear Motion.

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Unit 2 Linear Motion

I. Outline Motion defined Linear Motion Graphing Linear Motion Speed
Position vs. Time Linear Motion Graphing Linear Motion Speed Distance Displacement Velocity Acceleration

A. What is Relative Motion?

A. Motion Defined Does everything move? How would explain a car moving? If you place a book on your desk, is it in motion? Is motion relative? Yes, but relative to WHAT? .

The earth is moving around the sun, therefore, the book is moving relative to the sun
The car is moving relative to the road or track The space shuttle is moving relative to the Earth below. What do these two objects have in common? Distance from a reference point and time

1. Position vs. Time Position location relative to a fixed reference point Why a fixed reference point? farmer plowing furrows or a dancer Tells the kid to focus on a object on other side of field and not get distracted When finished lines all over. Why? What is wrong with this picture? Kid responds, “Cow kept moving.” Distance from a fixed point, a point that is not moving

B. What is Linear Motion? Motion means the rate at which something happens. E.g. How fast your car travels down the freeway…or this bird! Three components of rate: Speed Velocity Acceleration How do you know that the bird is moving and NOT just doing the “moonwalk” Why can’t you tell you are doing 400 mph in an airplane?

Simplest form of motion-moving along a straight line or path.
Horizontal or vertical but always a straight path Position relative to what? Movement relative to a motionless point Earth….. Sun…… Earth is spinning about 1000 mph or 460 meters per second- - what happens if the earth stops spinning??? Splat!-you are the bug on the windshield!

C. Graphing Linear Motion
y=mx+b or slope for a linear fit. You will be making graphs!!!! X and Y coordinates

D. Speed Speed Is the measure of how fast (the rate) something is moving Distance/time e.g. kilometer per hour or (km/h) covered 50 mph or 30 km/h Distance = miles Time hour

Average Speed: ( must be between largest & smallest numbers)
Instantaneous Speed: The speed at any given instant E.g. Cars accelerate and decelerate all the time while driving-stop light speed is 0 km/h, on the Autobahn a car may travel up to 130 km/h Average Speed: ( must be between largest & smallest numbers) How fast a car will travel over entire distance E.g. trip Average speed = total distance/ total time interval Ave. sp. 60 km/h if you traveled 240 km/4 h What is the speedometer on your car registering? What is the tachometer on your car registering?

How would you calculate average speed???

Practice Questions If the odometer reads 0 at the beginning of a trip and 35 km a half hour later(.5-hr), what is the average speed? Would it be possible to attain this average speed and never exceed a reading of 70km/h on the speedometer? d s t

Answers 35 km/0.5 h = 70 km/h Average speed=total distance/time interval (or m/s) No, not if the trip started at rest. instantaneous speed less than 70 km/h would have to be compensated with speeds greater than 70 km/h

E. How would you find distance???
Distance = average speed X time 70 km = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) km x 2h h Dist (m) S = d t Time (s) Speed (m/s)

Practice questions If a cheetah can maintain a constant speed of 25m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? d s t

Answer=Distance = average speed x the time interval
25 m/s X 10 s = 250m 25 m/s X 60 s = 1500m

Bowing Ball Velocity lab…and distance too?
Time to play! Speed lab and or bowling ball velocity

F. One more thing…Displacement
Displacement vs. distance Displacement is shortest distance traveled between all the points “as the crow flies” Distance is total distance traveled Driving distance

Map from mapquest. Point out start which is Davis high school, star should be davis, gray area where 273 is Davis high.

Distance vs. Displacement
Dave leaves his house to go to school. He drives to Leon’s house to get Leon. Then he drives to Jenna’s house to pickup Jenna. Then they all go to school. What distance has Dave traveled? What is Dave’s net displacement? Leon’s house Dave’s House

Distance and Displacement Defined
Distance = total amount of “ground covered” during a given time interval. E.g. a runner is at the 50 m mark at 1 s. Displacement = straight-line distance in a given direction from the starting point to the ending point for a given time interval. E.g. straight line from starting position DHS to ST George for ending position.

Time to Play! Displacement Lab
You will walk this out and measure with a meter stick. We will do the same lab again when we get to vectors and THEN we will add the math. GOT IT? Demo with motion sensor, track, and car

G. Velocity Speed in given direction e.g. 50 mp/h horizontal or vertical. Velocity is how fast and what direction “it” is moving e.g. car, boat, plane etc.

Constant vs. changing velocity
Constant=speed and direction are the same It is impossible to detect motion at constant speed. In a car you detect acceleration and negative acceleration (deceleration) Changing=one or both are changing e.g. accelerating

Question The speedometer of a car moving northward reads 60 km/h. It passes another car that travels southward at 60 km/h. Do both cars have the same speed, velocity?

Answer Same speed = yes both 60km/h
Same velocity = no, one northward, other southward

e. Velocity Equation Average velocity= change in distance/change in time, it is a ratio! Velocity means m/s v = ∆d / ∆t ∆d = d1 or f – d0 ∆t = t1 or f – t0 To give us meters per second

In physics average velocity involves:
Position (usually in meters) Time (seconds) Hence velocity is m/s It is the change in position divided by the time interval during which that change took place

Displacement Average Velocity
The average velocity equation rearranged v = ∆d / ∆t Times each side by ∆t v ∆t = ∆d v ∆t = d1 – d0 Add +d0 to each side to cancel out the minus d0 + v ∆t = d1

Velocity Questions A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go? Intuitively we know it is 4.0 m/s x 5 s = 20m Using our equation v = ∆d / ∆t Times each side by ∆t v∆t = ∆d v∆t = d1 – d0 Add +d0 to each side to cancel out the minus d0 + v∆t = d1

V = 4.0 m/s and is constant so no change
∆t = t1 – t0, which is 5.0 s – 0 s =5 s d0 = 0 Therefore: d0 + v∆t = d1 0 = (4.0 m/s) (5.0 s) = 20 meters

A bike accelerates from 0. 0 m/s to 4. 0 m/s in 4. 0 s
A bike accelerates from 0.0 m/s to 4.0 m/s in 4.0 s. What distance does it travel? d0 + v∆t = d1 0 + (4.0 m/s) (4 s) = 16 m

H. Acceleration Acceleration is the rate at which the velocity is changing… Formula = acceleration =change of speed/time interval Speed and velocity are measured in units of distance per time d/t (distance and time) Acceleration equation: a= ∆v/∆t = v1- v0/t1- t0

Acceleration…Question (concept)
Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40/km/h, then form 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration?

The speed increased by 5 km/h during each 1 second interval, thus, acceleration is 5 km/h during each interval…. help! We are now into acceleration

Acceleration = change of velocity / time interval
Acceleration is the rate at which velocity is changing with respect to time! e.g. you want to beat your friend to Atlantis Burger so you speed up and pass him on the frontage road! Acceleration = change of velocity / time interval IS negative acceleration real? YES!

Acceleration Question
In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?

Answer Acceleration = change in speed/time interval
15 km/h/5s = 3km/h/s Both are equal acceleration, rates of change the same Even thought speeds involved are quite different V1 – v0/ 5s (time between 2 points)

Time to play…graph matching

I. Summary: Rate of Change of Motion
The rate of change of distance with respect to time is speed. Pos. vs. time The rate of change of displacement with respect to time is velocity. m/s vs. time to find a distance The rate of change of velocity is acceleration. m/s vs. time to find a rate

Questions Chapter 2 from conceptual physics book (blue book)
Questions from chapter five, the red physics book pg 97 Chapter 5 questions and problems pg. 97: 17, 18, 23-28, 29 (calculator problem) 30, Pg 110: 33, 35 (no calculator manually make graph) 38, 40, and even problems 44, 46, 50, 54a, 58a

B. Free Fall Free fall (one-dimensional)
motion of any object under the influence of gravity only no air resistance or friction effects of any kind We are not going to do calculations involving air resistance If you jump off a chair, you are in free fall.

Conclusion: magnitude of acceleration is denoted by the symbol:
Galileo discovered (minus air resistance) freely falling objects had the same acceleration. He also discovered that the object, regardless of shape, size, height from which the object was dropped, thrown or even the mass acceleration was the same for all falling objects Paper and baseball demo After Galileo Isacc Newton proved Galileo’s theory Conclusion: magnitude of acceleration is denoted by the symbol: g = 9.81 m/s2

Review one dimension motion
Orange sheet review For free fall use the same formulas as before Now acceleration is g (9.80 m/s2 ) Acceleration is known due to gravity Key words: Dropped = 0 initial velocity Tossed = non zero initial velocity Fall or free fall = acceleration is g Velocity when object hits the ground = velocity at last instant before contact with ground is made

Time to play Pascal lab with free fall

Free Fall problems Chap. 5 questions Pg 106 Pg 113
31-33 Pg 113 66-70, 73 and 74

formulas v = gt v = instantaneous speed
g = acceleration ( 9.8 m/s2 ) force of gravity t = time Sometimes v=at (a is same as g)

formulas d = ½ gt2 d = distance object falls on the y axis
g = acceleration ( 9.8 m/s2 ) force of gravity t2 = time squared ½ (.5) x gt2

problem What would be the velocity of a falling rock starting from rest, 4s, 8s and 15s? v = (10 m/s2 ) (0s) = 0m/s V = (10 m/s2 )(4s) = 40m/s 80m/s and 150m/s Position and time

problems Find the speed required to throw a ball straight up and have it return 6s later. Neglect air resistance. Hint: v up = v down (3s + 3s) = 6s What is the velocity? Now solve for distance….. d = ½ gt2 Why ½? 3 seconds up and 3s seconds down

Table pg 17 and 20 Time Speed/velocity distance 0s 0ms 0m 1s 10m/s 5m
gt ½ gt2

Time to play!!! Free fall lab

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