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PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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MOTION ALONG A LINE Who’s Upside Down?

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MOTION ALONG A LINE Who’s Moving?

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MOTION ALONG A LINE Motion: 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: m displacement, s = x : change in position x = x f – x i displacement = final position – initial position

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MOTION ALONG A LINE displacement examples

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MOTION ALONG A LINE time, t: time since motion start, unit: s (text uses t) velocity, v: time rate of displacement, unit: m/s average velocity, v av = (x f -x i )/t has same +/- sign as displacement – shows direction of motion along line instantaneous velocity, v: actual velocity at a specific point in time, slope on an x vs. t graph. at constant speed, v=v av for changing speed, v v av

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MOTION 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/t a 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.

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SOLVING 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?

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GRAPHING MOTION interpreting an x vs. t (position vs. time) graph (moving forward) constant +v (not moving) constant v = 0 (moving backward) constant –v changing +v (speeding up) changing +v (slowing down)

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GRAPHING MOTION interpreting an x vs. t (position vs. time) graph for linear x vs. t graphs: rise = x x t run = t slope = rise/run = x/ t, so slope = v av

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GRAPHING MOTION interpreting an x vs. t (position vs. time) graph for curving x vs. t graphs: x t slope of tangent line = v instantaneous

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GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph (moving forward) constant +v (not moving) constant v = 0 (moving backward) constant –v changing +v (speeding up) changing +v (slowing down)

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GRAPHING MOTION comparing an x vs. t and a v vs. t graph

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ACCELERATION constant velocity constant acceleration

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ACCELERATION Acceleration, a: rate of change of velocity unit: (m/s)/s or m/s 2 speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?) average acceleration, a av = (v-u)/t = v/t instantaneous acceleration, a: actual acceleration at a specific point in time

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ACCELERATION Constant acceleration (a = a av ) example: a=2 m/s 2 time (s) speed (m/s ) position (m) v t, x t 2

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ACCELERATION terms: t: elapsed time x f : final position x o : initial position s: change in position (x f -x i ) terms: a: acceleration v avg : average velocity v f : final velocity u, v o : initial velocity v: change in velocity (v-u)

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ACCELERATION defined equations: a = v/t v av = x/t v av = (v+u)/2 derived equations: s = ½(v+u)t v = u + at x f = x i + ut + ½at 2 v 2 = u 2 + 2as

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GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph (speeding up) constant +a (constant speed) constant a = 0 (slowing down) constant –a For linear v vs. t graphs, slope = a

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GRAPHING MOTION comparing v vs. t and a vs. t graphs

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PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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FREE FALL Free Fall: all falling objects are constantly accelerated due to gravity acceleration due to gravity, g, is the same for all objects use y instead of x, up is positive g = –9.80 m/s 2 (at sea level; decreases with altitude)

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FREE FALL air resistance reduces acceleration to zero over long falls; reach constant, "terminal" velocity. Why does this occur? Air resistance is proportional to v^2

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PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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MOTION IN A PLANE Start at the Old Lagoon Go 50 paces East Go 25 Paces North Go 15 paces West Go 30 paces North Go 20 paces Southeast X marks the Spot!

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MOTION IN A PLANE Trigonometry sine: sin = opp/hyp cosine: cos = adj/hyp tangent: tan = opp/adj

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MOTION IN A PLANE Vectors scalars: only show how much (position, time, speed, mass) vectors: show how much and in what direction displacement, r or x : distance and direction velocity, v : speed and direction acceleration, a: change in speed and direction

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MOTION IN A PLANE Vectors arrows: velocity vector v = v (speed), (direction) length proportional to amount direction in map coordinates between poles, give degrees N of W, degrees S of W, etc. N S W E v

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MOTION IN A PLANE puck v relative to earth = puck v relative to table + table v relative to earth

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MOTION IN A PLANE Combining Vectors draw a diagram & label the origin/axes! Collinear vectors: v 1 v 2 v 1 v 2 resultant: v net =v 1 +v 2 (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?

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MOTION IN A PLANE Perpendicular vectors: resultant’s magnitude: resultant’s direction:

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PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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UNIT 1 TEST PREVIEW Concepts Covered: motion, position, time speed (average, instantaneous) x vs. t graphs, v vs. t graphs, a vs. t graphs vectors, scalars, displacement, velocity adding collinear & perpendicular vectors acceleration free fall, air resistance

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UNIT 1 TEST PREVIEW What’s On The Test: 21 multiple choice, 12 problems x = ½(v f +v i )tv f = v i + at x f = x i + v i t + ½at 2 v f 2 = v i 2 + 2a x

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