PHYSICS UNIT 1: KINEMATICS (Describing Motion)

1. PHYSICS UNIT 1: KINEMATICS (Describing Motion)

2. MOTION ALONG A LINE • Who’s Upside Down?

3. MOTION ALONG A LINE • Who’s Moving?

4. MOTION ALONG A LINE • Motion: change in position of an object compared toa 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 – xidisplacement = final position – initial position

5. MOTION ALONG A LINE • displacement examples

6. 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

7. 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.

8. 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?

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

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

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

12. 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) (not moving) (moving forward)

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

14. constant velocity constant acceleration ACCELERATION

15. 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

16. time (s) 0 1 2 3 4 5 6 speed (m/s) 0 2 4 6 8 10 12 position (m) 0 1 4 9 16 25 36 ACCELERATION • Constantacceleration (a = aav) example: a=2 m/s2 v  t, x  t2

17. 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

18. 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 ACCELERATION

19. 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 (slowing down) (speeding up) (constant speed)

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

21. PHYSICS UNIT 1: KINEMATICS (Describing Motion)

22. 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)

23. 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

24. PHYSICS UNIT 1: KINEMATICS (Describing Motion)

25. 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

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

27. 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

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

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

30. 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?

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

32. PHYSICS UNIT 1: KINEMATICS (Describing Motion)

33. 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

34. 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