4A. Motion DefinedDoes 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? .
5The earth is moving around the sun, therefore, the book is moving relative to the sun The car is moving relative to the road or trackThe space shuttle is moving relative to the Earth below.What do these two objects have in common?Distance from a reference point and time
61. Position vs. TimePosition location relative to a fixed reference pointWhy a fixed reference point?farmer plowing furrows or a dancerTells the kid to focus on a object on other side of field and not get distractedWhen 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
7B. 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:SpeedVelocityAccelerationHow 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?
8Simplest form of motion-moving along a straight line or path. Horizontal or vertical but always a straight pathPosition relative to what?Movement relative to a motionless pointEarth…..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!
9C. Graphing Linear Motion y=mx+b or slope for a linear fit.You will be making graphs!!!!X and Y coordinates
10D. SpeedSpeedIs the measure of how fast (the rate) something is movingDistance/time e.g. kilometer per hour or (km/h) covered50 mph or 30 km/hDistance = milesTime hour
11Average Speed: ( must be between largest & smallest numbers) Instantaneous Speed:The speed at any given instantE.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/hAverage Speed: ( must be between largest & smallest numbers)How fast a car will travel over entire distance E.g. tripAverage speed = total distance/ total time intervalAve. sp. 60 km/h if you traveled 240 km/4 hWhat is the speedometer on your car registering?What is the tachometer on your car registering?
13Practice QuestionsIf 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?ds t
14Answers35 km/0.5 h = 70 km/hAverage 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
15E. How would you find distance??? Distance = average speed X time70 km = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) km x 2hhDist (m)S = dtTime (s)Speed (m/s)
16Practice questionsIf 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?ds t
17Answer=Distance = average speed x the time interval 25 m/s X 10 s =250m25 m/s X 60 s =1500m
18Bowing Ball Velocity lab…and distance too? Time to play!Speed lab and or bowling ball velocity
19F. One more thing…Displacement Displacement vs. distanceDisplacement isshortest distance traveled between all the points“as the crow flies”Distance is total distance traveledDriving distance
20Map from mapquest. Point out start which is Davis high school, star should be davis, gray area where 273 is Davis high.
21Distance 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 houseDave’s House
22Distance 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.
23Time 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
24G. VelocitySpeed 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.
25Constant vs. changing velocity Constant=speed and direction are the sameIt 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
26QuestionThe 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?
27Answer Same speed = yes both 60km/h Same velocity = no, one northward, other southward
28e. Velocity EquationAverage velocity= change in distance/change in time, it is a ratio!Velocity means m/sv = ∆d / ∆t∆d = d1 or f – d0∆t = t1 or f – t0To give us meters per second
29In physics average velocity involves: Position (usually in meters)Time (seconds)Hence velocity is m/sIt is the change in position divided by the time interval during which that change took place
30Displacement Average Velocity The average velocity equation rearrangedv = ∆d / ∆tTimes each side by ∆tv ∆t = ∆dv ∆t = d1 – d0Add +d0 to each side to cancel out the minusd0 + v ∆t = d1
31Velocity QuestionsA 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 = 20mUsing our equationv = ∆d / ∆tTimes each side by ∆tv∆t = ∆dv∆t = d1 – d0Add +d0 to each side to cancel out the minusd0 + v∆t = d1
32V = 4.0 m/s and is constant so no change ∆t = t1 – t0, which is 5.0 s – 0 s =5 sd0 = 0Therefore: d0 + v∆t = d10 = (4.0 m/s) (5.0 s) = 20 meters
33A 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 = d10 + (4.0 m/s) (4 s) = 16 m
34H. AccelerationAcceleration is the rate at which the velocity is changing…Formula = acceleration =change of speed/time intervalSpeed and velocity are measured in units of distance per time d/t (distance and time)Acceleration equation:a= ∆v/∆t = v1- v0/t1- t0
35Acceleration…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?
36The 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
37Acceleration = 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 intervalIS negative acceleration real?YES!
38Acceleration 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?
39Answer Acceleration = change in speed/time interval 15 km/h/5s = 3km/h/sBoth are equal acceleration,rates of change the sameEven thought speeds involved are quite differentV1 – v0/ 5s (time between 2 points)
41I. Summary: Rate of Change of Motion The rate of change of distance with respect to time is speed.Pos. vs. timeThe rate of change of displacement with respect to time is velocity.m/s vs. time to find a distanceThe rate of change of velocity is acceleration.m/s vs. time to find a rate
42Questions Chapter 2 from conceptual physics book (blue book) Questions from chapter five, the red physics book pg 97Chapter 5 questions and problemspg. 97: 17, 18, 23-28, 29(calculator problem) 30,Pg 110: 33, 35 (no calculatormanually make graph) 38, 40, and even problems44, 46, 50, 54a, 58a
43B. Free Fall Free fall (one-dimensional) motion of any object under the influence of gravity onlyno air resistance or friction effects of any kindWe are not going to do calculations involving air resistanceIf you jump off a chair, you are in free fall.
44Conclusion: 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 objectsPaper and baseball demoAfter Galileo Isacc Newton proved Galileo’s theoryConclusion: magnitude of acceleration is denoted by the symbol:g = 9.81 m/s2
45Review one dimension motion Orange sheet reviewFor free fall use the same formulas as beforeNow acceleration is g (9.80 m/s2 )Acceleration is known due to gravityKey words:Dropped = 0 initial velocityTossed = non zero initial velocityFall or free fall = acceleration is gVelocity when object hits the ground = velocity at last instant before contact with ground is made
47Free Fall problems Chap. 5 questions Pg 106 Pg 113 31-33Pg 11366-70, 73 and 74
48formulas v = gt v = instantaneous speed g = acceleration ( 9.8 m/s2 ) force of gravityt = timeSometimes v=at (a is same as g)
49formulas d = ½ gt2 d = distance object falls on the y axis g = acceleration ( 9.8 m/s2 ) force of gravityt2 = time squared½ (.5) x gt2
50problemWhat would be the velocity of a falling rock starting from rest, 4s, 8s and 15s?v = (10 m/s2 ) (0s) = 0m/sV = (10 m/s2 )(4s) = 40m/s80m/s and 150m/sPosition and time
51problemsFind 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) = 6sWhat is the velocity?Now solve for distance…..d = ½ gt2Why ½?3 seconds up and 3s seconds down
52Table pg 17 and 20 Time Speed/velocity distance 0s 0ms 0m 1s 10m/s 5m gt½ gt2