1. Linear Motion Or 1 Dimensional Kinematics

2. 9/21  Pick Up Notes, Motion WS I, Formula Chart & Warm Ups. Get a calculator  Tests should be graded by Wednesday  If you were absent Friday you may take the test in class or after school today  WARM UP 1: Remember to write question & answer –The units for velocity are: –The units for acceleration are:

3. Great Website for Linear Motion Great Website for Linear Motion http://www.glenbrook.k12.il.us/gbssci /phys/class/1DKin/U1L1a.html http://www.glenbrook.k12.il.us/gbssci /phys/class/1DKin/U1L1a.html

4. Kinematics in one dimension  the study of linear motion (in a straight line -not curved)

5. Motion  What does it mean for an object to be in motion?  It is the change in position of an object as compared to a reference point *

6. Is the brick wall moving? Not from where she’s sitting, but…

7. …from space, the earth rotates and the wall with it. So, whether or not something is moving depends on your frame of reference. *

8. Frame of Reference  a fixed point used to determine magnitude and direction of motion  Magnitude?  See Video Here

9. How does speed differ from velocity?  Which one is scalar?  Which one is vector?

10. Sign for Vectors  the sign indicates direction  can be positive or negative  Right, East, or North are +  Left, West, or South are -

11. Have your formula chart out

12. Average Velocity  The average velocity of an object is defined as the displacement of an object divided by the time in which it took place. Average velocity =  v avg = = d 2 -d 1  t 2- t 1 Change in position Change in time dtdt* Does this look like the slope formula on a D v T Graph?

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14. Fill in the units meters______ seconds_____ meter per second ______ miles ______ hour______ miles per hour______ or ______ minutes______

15. Ex 1   A racing car driven by Speed E. Demon travels 480 kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s.

16. When doing calculations you must always include: FORMULA VARIABLES (KNOWNS) WORK (SUBSTITUTION) ANSWERUNITS

17. Ex 1 A racing car driven by Speed E. Demon travels 480 kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s. Step 3 Show substitution (with units) and answer 480 km= 240 km/hr v = 480 km= 240 km/hr 2 hrs 2 hrs Step 1 List Variables d= 480 km v = ? t = 2 hrs Step 2 Show Formula (arranged to solve for unknown) v = d t Step 4 This problem requires dimensional analysis 240km 1000m 1hr = 66.67 m/s 1 hr 1 km 3600s

18. Ex. 2 Sunday Driver takes her Cadillac for a spin and travels 50.0 km at an average speed of 35.0 m/s. How long (in seconds) was she driving her car? There are two ways to approach this…….

19. Ex. 2 Sunday Driver takes her Cadillac for a spin and travels 50.0 km at an average speed of 35.0 m/s. How long (in seconds) was she driving her car? VariablesFormulaWork Answer & Unit d= 50 km v = 35 m/s v = d/t t = d/v t= (50 km)/(35 m/s) ???? t= (50000m)/(35 m/s) t= 1428.57 sec

20. Ex. 2 Sunday Driver takes her Cadillac for a spin and travels 50.0 km at an average speed of 35.0 m/s. How long (in seconds) was she driving her car? VariablesFormulaWork Answer & Unit d= 50 km v = 35 m/s Use Dimensional Analysis t= 1428.57 sec 50 km1000 msec 1 km35 m

21. Ex 3   A car travels at a constant speed of 4m/s for 5s. How far does it go in m?

22. Ex. 3   A car travels at a constant speed of 4m/s for 5s. How far does it go in m?VariablesFormulaWork Answer & Unit v= 4m/s t = 5 s v = d/t d = vt d= (4m/s)(5s) d = 20 m

23. Acceleration  change in velocity divided by change in time (a = ∆v/∆t)  Where  ∆v = (v final -v initial )  ∆t =(t final -t initial )  vector quantity  SI units include m/sec 2 or cm/sec 2

24. Acceleration  Mathematically,  Avg acceleration =  a avg = = = Change in velocity Change in time vtvt v f - v i t f - t i* v f - v i t Does this look like the slope formula on a V v T Graph?

25. Ex 4   A rocket takes off from rest from the launching pad. It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket?

26. Ex 4 Ex 4 A rocket takes off from rest from the launching pad. It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket? Step 3 Show substitution (with units) and answer 150 m/s - 0m/s = 15 m/s 2 a = 150 m/s - 0m/s = 15 m/s 2 10 sec 10 sec Step 1 List Variables d= v i = 0m/s (at rest) v f = 150 m/s a= ? t = 10 sec Step 2 Show Formula (rearranged) a = v f – v i t

27. Ex 5   Suppose a treadmill has an average acceleration of 4.7 m/s 2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds?

28. Ex 5 Ex 5 Suppose a treadmill has an average acceleration of 4.7 m/s 2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds? Step 3 Show substitution (with units) and answer v f 1.7m/s + [(150 sec) v f = 1.7m/s + [(4.7 m/s 2 )(150 sec) v f = 706.7 m/s v f = 706.7 m/s Step 1 List Variables d= v i = 1.7 m/s v f = ? a= 4.7 m/s 2 t = 150 sec Step 2 Show Formula (rearranged) v f = v i + at

29. Acceleration equations  Remember velocity, displacement, and acceleration are all vector quantities.  Indicate direction  right or east: positive  left or west: negative

30. With a little algebra when we combine the velocity equation and the acceleration equation we have the following:

31.  v avg = Δd/Δt  a = Δv/Δt = v f – v i /t  a = v f 2 - v i 2 2Δd  Δd = v i Δt + ½aΔt 2  Δd = v i Δt +.5aΔt 2 a – acceleration in m/s 2 v - change in velocity in m/s vf – final velocity in m/s vi – initial velocity in m/s t or t – time interval in seconds d – displacement in m

32. Any of these formulas can be rearranged!!!  How do we know which formulas to use?  DVVAT!!!!!

33. Example 6   A tricycle, initially traveling at 0.15 m/s, experiences an acceleration of 0.045 m/s 2.   What is the velocity of such tricycle after a period of 15 seconds?   List your knowns (DVVAT)   Determine Formula   Rearrange   Substitute and solve

34. Example 6 v i = 0.15 m/s a = 0.045 m/s 2 t = 15 s v f = ? What equation? a = v f – v i t Rearrange it for v f v f = v i + aΔt v f = v f = 0.15 m/s +( 0.045 m/s2)(15 s) v f = 0.83 m/s

35. Example 7 A bowling ball decelerates. If it slows from 15.3 m/s to 2.77 m/s in 14.0 seconds, what is the measure of such deceleration?   List your knowns (DVVAT)   Determine Formula   Rearrange   Substitute and solve

36. Example 7 v i = 15.3 m/s v f = 2.77 m/s t = 14.0 s a = ? What equation? a = v f – v i t Solve for a v f = v i + aΔt v f - v i = aΔt (v f – v i )/Δt = a a = (2.77 m/s a = (2.77 m/s – 15.3 m/s)/(14.0 s) a= -0.895 m/s 2

37. Example 8 An arrow takes a horizontal path the arrow slows from 26.3 m/s to 15 m/s during flight with an acceleration of -0.83 m/s 2. How far does it travel?   List your knowns (DVVAT)   Determine Formula   Rearrange   Substitute and solve

38. Example 8 v i = 26.3 m/s v f = 15 m/s a = -0.83 m/s 2 d = ? What equation? a=v f 2 - v i 2 / 2Δd Solve for d d=v f 2 - v i 2 / 2a d = (15 m/s) 2 -(26.3 d = (15 m/s) 2 -(26.3m/s) 2 /(2 x-0.83 m/s 2 ) d= 281.14 m

39. Vertical Acceleration  Show video on You Tube  Feather in a vacuum https://www.youtube.com/watch?v=c jSvxWpbP_o

40. Free Fall  In the absence of air resistance all objects dropped near the surface of a planet fall with the same constant acceleration.

41. Free fall acceleration  Also called acceleration due to gravity  denoted with the symbol g.  g = 9.8m/s 2,  since it is natural to fall down, we will refer to the down direction as +  g = a = 9.8m/s 2

42. Acceleration due to Gravity  What does it look like related to speed?

43. If a ball was simply dropped

44. Freefall Practice Ex 9  Dylan sits in a tree dropping acorns on people walking by. If the acorns take 2.6 sec to hit the ground, how tall is the tree in which Dylan is sitting?  List your knowns! D-V-V-A-T  What formula will you use?

45. d = ? v i = 0 m/s (0 VELOCITY BEFORE IT DROPS! vfvfvfvf a = 9.8 m/s 2 (Acceleration due to gravity) t = 2.6 sec

46.  What formula?  d = v i t +.5at 2  Remember since v i =0 v i t=0  d =.5at 2  d = (.5)(9.8m/s 2 )(2.6s) 2  d = 33.1m

47. Ex10  A flowerpot falls from a windowsill 55.0m above the sidewalk below. 1)How long do the people below have to move out of the way? 2)How fast is the flowerpot going when it hits the ground?

48. Natalie is frustrated in Physics. She throws her pencil downward with an initial velocity of.68m/s. Her hand is 80cm above the floor. What is the velocity of the pencil in m/s just before impact? Ex 11

49. Ex 12 Brent is hanging over the bleachers at a soccer game. He opens his mouth to yell at someone and his gum falls out of his mouth straight down!!!! What is the velocity of the gum when it strikes the ground 15m below?

50. A boy is spinning on a merry-go-round at constant speed of 0.5 m/s. Describe his velocity. Describe his acceleration.

51. Hot Wheels Track