4MOTION ALONG A LINEMotion: change in position of an object compared to a frame of reference (a "stationary" reference point)Measuring Motion (along a line)position, x: location with respect to the origin The origin is (x=0), unit: mdisplacement, s = Dx : change in positionDx = xf – xi displacement = final position – initial position
6MOTION ALONG A LINEtime, t: time since motion start, unit: s (text uses Dt)velocity, v: time rate of displacement, unit: m/saverage velocity, vav = (xf-xi)/thas same +/- sign as displacement – shows direction of motion along lineinstantaneous velocity, v: actual velocity at a specific point in time, slope on an x vs. t graph.at constant speed, v=vavfor changing speed, vvav
7MOTION ALONG A LINE Speed: the amount of velocity S=d/t Velocity is speed and direction (+/- along a line), speed doesn’t have direction. V=∆x/ta velocity of -24 m/s is not the same as +24 m/s (opposite directions), but both have the same speed (24 m/s).car speedometer indicates speed only; for velocity, you would need a speedometer and a compass.
8SOLVING PROBLEMS Problem-Solving Strategy Given: What information does the problem give me?Question: What is the problem asking for?Equation: What equations or principles can I use to find what’s required?Solve: Figure out the answer.Check: Do the units work out correctly? Does the answer seem reasonable?
9GRAPHING MOTION interpreting an x vs. t (position vs. time) graph constant +vconstant v = 0constant –vchanging +vchanging +v(moving forward)(not moving)(moving backward)(speeding up)(slowing down)
10GRAPHING MOTION slope = rise/run = Dx/Dt, so slope = vav interpreting an x vs. t (position vs. time) graphfor linear x vs. t graphs:xtslope = rise/run = Dx/Dt, sorise = Dxslope = vavrun = Dt
11GRAPHING MOTION slope of tangent line = vinstantaneous interpreting an x vs. t (position vs. time) graphfor curving x vs. t graphs:xtslope of tangent line = vinstantaneous
12GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph constant +vconstant v = 0constant –vchanging +vchanging +v(slowing down)(moving backward)(speeding up)(moving forward)(not moving)
13GRAPHING MOTIONcomparing an x vs. t and a v vs. t graph
15ACCELERATION Acceleration, a: rate of change of velocity unit: (m/s)/s or m/s2speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?)average acceleration, aav = (v-u)/t = Dv/tinstantaneous acceleration, a: actual acceleration at a specific point in time
16ACCELERATION Constant acceleration (a = aav) v t, x t2 example: a=2 m/s2time (s)12345624681012speed (m/s)position (m)149162536v t, x t2
17ACCELERATION terms: terms: t: elapsed time xf : final position xo: initial positions: change in position (xf-xi)terms:a: accelerationvavg: average velocityvf: final velocityu, vo: initial velocityDv: change in velocity (v-u)
18ACCELERATION defined equations: a = Dv/t vav = Dx/t vav = (v+u)/2 derived equations:s = ½(v+u)tv = u + atxf = xi + ut + ½at2v2 = u2 + 2as
19GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph For linear v vs. t graphs, slope = aconstant a = 0constant +aconstant –a(speeding up)(slowing down)(constant speed)
20GRAPHING MOTIONcomparing v vs. t and a vs. t graphs
22FREE FALLFree Fall: all falling objects are constantly accelerated due to gravityacceleration due to gravity, g, is the same for all objectsuse y instead of x, up is positiveg = –9.80 m/s2 (at sea level; decreases with altitude)
23FREE FALLair resistance reduces acceleration to zero over long falls; reach constant, "terminal" velocity.Why does this occur?Air resistance is proportional to v^2
25MOTION IN A PLANE Start at the Old Lagoon Go 50 paces East Go 25 Paces NorthGo 15 paces WestGo 30 paces NorthGo 20 paces SoutheastX marks the Spot!
26MOTION IN A PLANE sine: sin q = opp/hyp cosine: cos q = adj/hyp Trigonometrysine: sin q = opp/hypcosine: cos q = adj/hyptangent: tan q = opp/adj
27MOTION IN A PLANE Vectors scalars: only show how much (position, time, speed, mass)vectors: show how much and in what directiondisplacement, r or x : distance and directionvelocity, v : speed and directionacceleration, a: change in speed and direction
28MOTION IN A PLANE q v Vectors arrows: velocity vector v = v (speed), q (direction)length proportional to amountdirection in map coordinatesbetween poles, give degrees N of W, degrees S of W, etc.qvNSWE
29MOTION IN A PLANEpuck v relative to earth = puck v relative to table + table v relative to earth
30MOTION IN A PLANE Combining Vectors draw a diagram & label the origin/axes!Collinear vectors: v v v v2resultant: vnet=v1+v (direction: + or –)ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?ex: A plane flies 40 m/s E with a 10 m/s E tailwind. What is the net velocity?
31MOTION IN A PLANE Perpendicular vectors: resultant’s magnitude: resultant’s direction:
33UNIT 1 TEST PREVIEW Concepts Covered: motion, position, time speed (average, instantaneous)x vs. t graphs, v vs. t graphs, a vs. t graphsvectors, scalars, displacement, velocityadding collinear & perpendicular vectorsaccelerationfree fall, air resistance
34UNIT 1 TEST PREVIEW What’s On The Test: 21 multiple choice, 12 problemsDx = ½(vf+vi)t vf = vi + atxf = xi + vit + ½at2 vf2 = vi2 + 2aDx