PHYSICS UNIT 1: KINEMATICS (Describing Motion)

MOTION ALONG A LINE Who’s Upside Down?

MOTION ALONG A LINE Who’s Moving?

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 = Dx : change in position Dx = xf – xi displacement = final position – initial position

MOTION ALONG A LINE displacement examples

MOTION ALONG A LINE time, t: time since motion start, unit: s (text uses Dt) velocity, v: time rate of displacement, unit: m/s average velocity, vav = (xf-xi)/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=vav for changing speed, vvav

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.

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?

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

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

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

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

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

ACCELERATION constant velocity constant acceleration

ACCELERATION Acceleration, a: rate of change of velocity unit: (m/s)/s or m/s2 speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?) average acceleration, aav = (v-u)/t = Dv/t instantaneous acceleration, a: actual acceleration at a specific point in time

ACCELERATION Constant acceleration (a = aav) v  t, x  t2 example: a=2 m/s2 time (s) 1 2 3 4 5 6 2 4 6 8 10 12 speed (m/s) position (m) 1 4 9 16 25 36 v  t, x  t2

ACCELERATION terms: terms: t: elapsed time xf : final position xo: initial position s: change in position (xf-xi) terms: a: acceleration vavg: average velocity vf: final velocity u, vo: initial velocity Dv: change in velocity (v-u)

ACCELERATION defined equations: a = Dv/t vav = Dx/t vav = (v+u)/2 derived equations: s = ½(v+u)t v = u + at xf = xi + ut + ½at2 v2 = u2 + 2as

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

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

UNIT 1: KINEMATICS (Describing Motion) PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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/s2 (at sea level; decreases with altitude)

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

UNIT 1: KINEMATICS (Describing Motion) PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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!

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

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

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

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

MOTION IN A PLANE Combining Vectors draw a diagram & label the origin/axes! Collinear vectors: v1 v2 v1 v2 resultant: vnet=v1+v2 (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?

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

UNIT 1: KINEMATICS (Describing Motion) PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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

UNIT 1 TEST PREVIEW What’s On The Test: 21 multiple choice, 12 problems Dx = ½(vf+vi)t vf = vi + at xf = xi + vit + ½at2 vf2 = vi2 + 2aDx