#### Read Microsoft PowerPoint - Physics111F9 L02.ppt text version

`Lecture 2 (Walker: 2.1-2.3) Position, Displacement, Speed, and VelocityAugust 31, 2009Some illustrations courtesy Prof. J.G. Cramer, U of Washington1Physics Readiness Test· Results posted on course web page and on bulletin board across from Thornton 118 · &quot;Pass&quot; status -- Wait list students who passed will get an add permit · &quot;Fail&quot; status -- You will be dropped from Phys 111/112. · &quot;ALEKS&quot; status -- You will be dropped, but can get an add permit by achieving 80% or better proficiency in ALEKS (see course web page). Continue attending class and doing homework.2Scalar and Vector Quantities· Scalar quantities are completely described by magnitude only (temperature, length,...) · Vector quantities need both magnitude (size) and direction to completely describe them (force, displacement, velocity,...)r · Write vector as v­ Represented by an arrow; the length of the arrow is proportional to the magnitude of the vector ­ Head of the arrow shows the direction(or sometimes v)3Temperature: Scalar Quantity; specified by single number giving its magnitude.Wind Velocity: Vector Quantity; specified by its magnitude &amp; direction.45Chapter 2 One-Dimensional (1-D) KinematicsOne dimensional kinematics refers to motion along a straight line. Terms we will use:· Position, distance, displacement · Speed, velocity (average and instantaneous) · Acceleration (average and instantaneous)6Coordinate SystemsA coordinate system is used to describe location, or position. A coordinate system consists of:­ a fixed reference point called the origin (e.g., metal disk in street, center of table) ­ a set of axes and definition of &quot;positive&quot; directions (e.g., &quot;x axis points East&quot;) ­ the units for the axes (e.g., meters) The position of an object is its location in a coordinate system. Position is a vector quantity7Cartesian coordinate system· Also called rectangular coordinate system · x- and y- axes · position points are labeled (x,y)The arrow on axis indicates the &quot;positive&quot; direction.8Plane polar coordinate system­ origin and reference line are noted ­ point is distance r from the origin in the direction of angle , ccw from reference line ­ position points are labeled (r,)9SFSU: 37.72084N, -122.476619E10Position· Position is defined in terms of a frame of reference (coordinate system) · Frame A: xi &gt;0 and xf &gt;0 Frame B: x'i&lt;0 but x'f &gt;0 Note that we use subscripts to indicate different positions:Axi By'xfxi initial position (or x0) xf final position; x2 position #2· Vector quantity; in 1-dim, usually use + or - to specify direction and write as just x (no arrow) · SI Unit for position amount: meter (m)x'x i'O'xf'11Displacement· Displacement measures the change in position­ Represented as x (if horizontal) or y (if vertical) xx = x f - xi­ Vector quantity; + or generally sufficient to indicate direction for 1dimensional motion ­ Sometimes write asxiSI Units: Meters (m)xfr r r x = x f - xi12DistanceDistance (scalar) is the total length of travel. SIunit: m If you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi.13Displacement vs. Distancehas a direction (maybe just + or - in 1-D).Displacement is the net change in position, andYou drive from your house to the grocery store and then to your friend's house, your net displacement is -2.1 mi:x = x f - xi = 0 - 2.1mi = -2.1miThe distance you have traveled is 10.7 mi.xfxi14Distance &amp; Displacement?· Distance may be, but is not necessarily, the magnitude of the displacementDisplacement(orange line)Distance(blue line)15Position-time graphsNote: position-time graph is not necessarily a straight line, even though the motion is along x-direction16Average SpeedThe average speed (SI unit: m/s; scalar or vector?) is defined as the distance traveled divided by the time the trip took: Average speed = distance / elapsed time Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h? Could average speed ever be negative?17Average Velocity· Say takes time t for an object to undergo a r displacement x · The average velocity is rate at which the displacement occurs r r rr x x f - xi = vaverage = t t· SI Unit: m/s · It is a vector; direction will be the same as the direction of the displacement (t is always positive) · + or - is sufficient direction description for 1-D motion; sovaverage =x x f - xi = t t18Average Speed and VelocityAverage velocity = displacement / elapsed time If you return to your starting point, your average velocity is zero. t=8s8svrun =vwalk =x 50.0 m-0 = =6.25 m /s t 8.0 s-0x 0-50.0 m = =-1.25 m /s t 48.0 s-8.0 s48 s t=48svav =x 0 = = 0.0 m/s t 48.0 s -019Average Speed and VelocityAvg. speed may be, but is not always, the magnitude of avg. velocity Graphical Interpretation of Average Velocity: The same motion, plotted one-dimensionally and as a two dimensional x-t graph:Average speed (0-4s) = (7m)/(4s) = 1.75 m/sAverage velocity (0-4 s) = ?20Average Speed and VelocityAverage speed may be, but is not necessarily, the magnitude of avg. velocity Graphical Interpretation of Average Velocity: The same motion, plotted one-dimensionally and as a two dimensional x-t graph:Average speed (0-4s) = (7m)/(4s) = 1.75 m/sAverage velocity (0-4 s) =(-2 m)/(4 s) = - 0.5 m/sSlope of line = average velocity21Instantaneous VelocityDefinition:r r x v = lim t 0 t(2-4)This means that we evaluate the average velocity over a shorter and shorter period of time; as that time becomes infinitesimally small, we have the instantaneous velocity. The instantaneous velocity gives the speed and direction of motion at each instant. What about instantaneous speed? Same as instantaneous velocity? What is the &quot;speedometer&quot; in a car measuring?22Graphical Interpretation of Average &amp; Instantaneous Velocityvavg = x2 - x1 t 2 - t1x1vavg =x3 - x2 t3 - t 2x2 x323Instantaneous VelocityThis plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity at time t is the slope of the line tangent to the curve at t.24Calculating Instantaneous Velocity25Velocity &amp; SlopeThe position vs. time graph of a particle moving at constant velocity has a constant slope.The position vs. time graph of a particle moving with a changing velocity has a changing slope.4.5 m3.0 s slope = velocity = 4.5 m/3.0 s = 1.5 m/s26Key Points of Lecture 2· Scalarsand Vectors·Coordinate Systems·Position ( x; xi, xf ) &amp; Displacement ( x ) ·Average Speed ( vavg ) &amp; Velocity ( vavg ) ·Instantaneous Speed ( v ) and Velocity (rrr v)·Relation between velocity &amp; slope of position-time plot Before the next lecture, read Walker, 2.4 - 2.6. Homework Assignment #2a is due at 11:00 PM on Wednesday, Sept. 2.27`

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