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Kinematics (Unit 2).pdf

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Department
Physics
Course
PHYSICS 1L03
Professor
Reza Nejat
Semester
Fall

Description
Motion Kinematics Locomotion Chapter 2 What is motion? Concepts: Position & Displacement Velocity & Speed Acceleration •Mtagfit.ie Motion in one Dimension Free Fall Physiological Detection of Acceleration PHYS 1L03, Fall 2013, McMaster University, R. Nejat Motion Motion http://www.imagekind.com/child-skipping-down-alley-art?IMID=642437f1-365b-4f63-988f-a5e712155344 A child skipping down alley. Can we analyze its motion? Can we analyze its motion? PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 1 Motion Motion The bird’s flight! The bird’s flight! Q: What kind of A: motion can you verify for this bird’s flight? These images of a bird in flight show the bird’s What kind of motion can you verify for this bird’s flight? position as a function of time. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat Motion One-Dimensional (1D) Motion •Im i,delti: •Piin –Whereistheobject? –referstoanobjectlocationrelativetosome •Position origin or reference point. –Howfarhastheobjectmovedfromwhere is was? •Displacement 0 1 2 3 4 x1 –Howfastisthemotion? 1 2 4 x •Velocity 0 3 2 –Isthemotiongettingfasterorslower? sttih different in these two •Acceleration coordinate systems with two different origins. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 2 One-Dimensional Motion One-Dimensional (1D) Motion •Veordcarati:t •Pive)r –anobjectlocationrelative to some origin or reference point, shown as a vector. •Veo:r is a quantity that has both a magnitude and a direction. ▯ x –Positionisavectorquantity. 0 1 2 3 4 x1 ▯ x •Sca:r is a quantity with no direction. x2 –Themassofanobjectisascalarquantity. -2 -1 0 1 2 PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion •Dilemete)r Distance: octt•sc –referstothechangein an object’s position along the actual path used to connect them. ▯ ▯ ▯ ▯ x ▯ x ▯ x Displacement vs. Distance: f i lfia ent of an object is not the same as the distance it travels. ▯ x x 0 xi i x xf Example: f x ▯ x ▯ x▯ x 0 xf xf xi f i xi ▯ ▯ ▯ ▯ x▯ xf▯xi PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 3 One-Dimensional (1D) Motion One-Dimensional Motion •saemet •OnDienilm)iabe described by scalars (real numbers –Inonedimension(1D) ▯ x with units) as functions of time. –e.g. x(t) x 0 xi xf •Teiptrgi)es track of direction. ▯ x ▯ x ▯fx i • f stands for final and i stands for initial. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion Motion ailib coordinate system •Dilm nt) ▯ x ▯ x ▯ f i – indicates the motion is in the –ACoordinatesystem ▯ x ▯ 0 •hasii,l(unt)tiitinieco positive x direction. –Positionaxis x x x •ilethatpassi,illtoghtheorg 0 i f the positive direction of motion – ▯ x ▯ 0 indicates the motion is in the •In 1 D, this is called x-axis negative x direction. •Thiiatx=0 –Timeaxis 0 xf xi x •hasii(t=l(s,ortinr),adrieco indicating increasing value of time PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 4 Motion One-Dimensional Motion X (cm) •Cott: •nuah: T (s) •Tgsw-e position of an object as a function of time. •jititte increases. •jeflts decreases. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion Position vs time graph Example: X(km) T(min) •oit-e X(km) T(min) +3 0 10 graph +3 0 +3 10 0 +3 10 +10 23 –Thepositionofatrainat +10 28 various time is given at the +10 23 -10 table, draw the position vs. 0 40 +10 28 -26 56 Position x (km) time graph for it. -20 0 40 -26 56 -30 0 10 20 30 4050 60 Time t (min) PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 5 One-Dimensional Motion One-Dimensional Motion Average Velocity: defined as Velocity: ▯ ▯ ▯ ▯ x fx i ▯x •it.r vaverage ▯ tf▯ t i ▯t •ctofdittn object is moving. •tie rate of change of an object’s displacement. •Deedbtiemetd the time interval Position-versus-time graph PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion ▯ ▯ ▯ Average Velocity: vaveragexf▯xi▯ ▯x f ▯ i ▯t Example: x ▯ x ▯ x vaverage 2 1 ▯ 41:3 tA .ot lHh uorht sespniart•A t2▯ t1 ▯t p.m., the train is 3 km east of the city centre. (omitting vector signs). B At 3:56 p.m., the train is 26 km west of the •icil city centre. What is the average velocity of slop of the straight line the train during this interval? connecting two points on the position vs time A graph. •fin v is m/s PHYS 1L03, Fall 2013, McMaster University, R. Nejat graph PHYS 1L03, Fall 2013, McMaster University, R. Nejat 6 One-Dimensional Motion One-Dimensional Motion Average speed: Example: distance distance vavgspeed▯ ▯ t2▯ t 1 ▯t •aid – Is always positive itira speed (v avg) •ti v is m/s PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion Instantaneous Velocity: Instantaneous Velocity: ▯ x d x vins2 ) = slope of this line v ▯ lim ▯ (tangent to the carve) inst ▯t▯0 ▯ t d t ▯ x d x rrby vinst ▯ ▯t▯0 ▯ the slope of a line x (m) ▯ t d t tangent to the (omitting vector signs). curve on the position-versus- nvil time graph at any time is the slope of a line tangent to the position-versus-time graph at that time. t (sec) PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 7 One-Dimensional Motion One-Dimensional Motion Example: Example: • Use the position vs. time graph for a train to estimate its velocity in km/h at t = 40 min. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion Example: Example: elra•ieT a function of time is given by the curve shown below. Find the velocity at t=2 s? instantaneous velocity at time t = 2 s. When is the velocity greatest? When is it zero? Is it ever negative? What is the average velocity of this particle between t = 2 s and t = 5s? Greatest velocity ? PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 8 One-Dimensional Motion One-Dimensional Motion Example: Zero velocity? Negative velocity? Average velocity? tig peed, how an African lion can catch a Cape buffalo? PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion Acceleration: •AAtlc ▯ ▯ ▯ ▯ vf i ▯v vf •etr . aaverage▯ Xf f i t ▯ •chwsihitc an object’s velocity is changing. •Ictl ▯ •i rate of change of velocity. ▯ ▯ v Xi vi ainst▯ ▯t▯0 t t ▯t i fi •Dpnobtydte time interval. PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat 9 One-Dimensional Motion One-Dimensional Motion •Agtlc •Aaeilt: v 2▯ v1 ▯ v v2▯ v 1 ▯v a avg▯ ▯ a average ▯ t2▯ 1 ▯t t2▯ t1 ▯t v2 •Ieyd the slope of the (omitting vector signs) velocity straight line •Iitl connecting two B ▯v points on the v2 velocvty ainst▯ ▯t▯0 v1 velocity-versus-time v1 A ▯t time graph. 1 t2 (omitting vector signs) 2 • Unit of a is m/s PHYS 1L03, Fall 2013, McMaster University, R. Nejat PHYS 1L03, Fall 2013, McMaster University, R. Nejat One-Dimensional Motion One-Dimensional Motion B C D ▯ v Example: x •toclt: ainst lim ▯t▯0▯t •rs x(t), v(t), a(t) • The position-versus-time E peby A t the slope of a line graph of an object moving along x-axis is v tangent to the given. curve on the t aA velocity-versus- A B aB – Draw the velocity- time graph. versus time graph, v(t). a – Draw the acceleration- t versus-time graph, a(t). PHYS 1L03, Fall 2013, McMaster
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