Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 241Looking Back:What is a motion diagram? What is particle model?What are basic elements of a coordinate system?Distance and displacement2Looking Back:A motion diagram is a composition image showing an object’s position at several equally spaced instants of time.In Particle model the object is treated as if all its mass were concentrated at a single point called a particle. Position: where the location of the object.A coordinate system contains: an origin point, axes with scale, direction and unitOne -dimensional coordinate system using an x-axis origin, scale, unitsx (m)050100 150-50-100Distance, Displacement, Speed and Velocity 3Distance is actual length of an object traveled regardless of its direction. A scalarDisplacement: is a change of position including the direction of motion. A vector∆x = xf – xi1. Alice is sliding along a smooth, icy road on her sled when she suddenly runs headfirst into a large, very soft snowbank that gradually brings her to a halt. Draw a motion diagram for Alice. Show and label all displacement vectors.42. Maria is at position x = 23 m. She then undergoes a displacement ∆x = –50 m. What is her final position?A. –27 mB. –50 mC. 23 mD. 73 mAnswer to Checking Understandingmmmxmxmff2750232350Goals for todayScalars and vectorsA sense of scale:•Significant figures•Scientific notation•SI Units5Physical quantities:•Position•Distance •Displacement•Speed •VelocityDefinition, notation and applicationIn BriefBefore next Tuesday: Review Ch.1 (Quiz-1 next Tuesday) Read: Chapter 2, sections 1~3 Student Workbook Ch.1, problems 19~22 MP HW 2: Math Review available tomorrowDistance, Displacement, Speed and Velocity 6Distance is actual length of an object traveled regardless of its direction. ScalarDisplacement: is a change of position including the direction of motion. Vector(1.1)A change in any quantity is the final value of the quantity minus its initial value speed distance traveled in a given time intervaltime interval)2.1(intervaltimentdisplacemetxvelocitySpeed: a scalarThe car moves 40 m in 1 s. Its speed is = 4040 m1 smsThe bike moves 20 m in 1 s. Its speed is = 2020 m1 sms7(m)Motion diagrams for a car and a bicycleVelocity: a vector8(m)Two bicycles traveling at the same speed, but with different velocities.An object’s velocity vector points in the same direction as its displacement vector.Motion diagrams for two bicyclessmssmmBike/201220401smssmmBike/201310060291. How much distance did you travel to school today and in how much time? What was your average speed?2. You go from home to school and then back home in the evening. What total distance did you travel? What is your net displacement? What is the velocity of a round trip?QuestionsScalars and vectors10Scalar quantities can be expressed by a single number (with a unit). • Time, distance, speed, temperature… are scalars. • A scalar can be positive, negative, or zero.Vector quantities need both a magnitude and direction. • Displacement, velocity, acceleration, force… are vectors. • The magnitude of a vector can be positive and zero, not negative. magnitude (length)NotationDirectionAVectors11These vectors are equalThese vectors are differentAre these vectors equal or different?ABCABCCBAVectors12A displacement vectordrawn from the initial to the final position.pointing the final position.The displacement vector of a car: initial point A, final point B.Regardless of the actual path.ABVectors13A velocity vector: pointing the direction of the motionABVectorsVelocity VectorsDisplacement VectorsIn motion diagrams14Example: Velocity VectorsJake throws a ball at a 60° angle, measured from the horizontal. The ball is caught by Jim. Draw a motion diagram of the ball with velocity vectors.15Vector AdditionExample of sum of two vectors16Sam undergoes two displacementsVectorsSum of two vectors: Adding Vectors Graphically17Example: Adding Displacement VectorsJenny runs 1 mi to the northeast, then 1 mi south. Graphically find her net displacement.18Vectors19A vector can be decomposed into its componentsA two-dimensional coordinate systemoNeed trigonometryHow to compute lengths (magnitude) and angles (direction) of triangles? AxAyAxyyxAAAVectors and Trigonometry20Also review Pythagorean theorem:HOsinHAcosAOtan222OAH 21oVectors and TrigonometryHOsinHAcosAOtan222OAH AxAyAxy222yxAAA xyAAtanAAysinAAxcos22Stop to think 1.5: P and Q are two vectors of equal length but different direction. Which vector shows the sum of P+Q?1. How many significant figures does each of the following numbers have?a. 6.21______ c. 6210.0______ e. 6.21x103 ______ b. 0.0621______ d. 1.0621______ f. 6.21x10-3 ______2. Compute the following numbers, applying the significant figure standards adopted for this text.c. 33.3x25.4= b. 33.3-25.4= C. (4.32x1.23)-5.1 =3. Express the following numbers and computed results in scientific notation, paying attention to significant figures.d. 9,827= b. 0.000000550= c.3,200,000=4. Convert the following to SI units:a. 9.12µs= b. 3.42km= c. 80km/hr=Take home quiz (due next Tuesday, Jan. 21st)– from Student Workbook 1.14—1.17Refer to section 4 in Ch.1: A sense of scale.24 Student Workbook problems: Chapter 1 1-3, 6-8,10 and 12 19~22 NewReminder: Take Home Quiz due next