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Linear Motion

Linear Motion. Fast. S peed depends on distance and time Average speed uses total distance and total time Use this when an object travels at different speeds. Scalars vs . Vectors. Scalars : measure the amount (magnitude) ex: distance traveled temperature speed limits

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Linear Motion

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  1. Linear Motion

  2. Fast • Speed • depends on distance and time • Averagespeed • uses total distance and total time • Use this when an object travels at different speeds

  3. Scalars vs. Vectors • Scalars: measure the amount (magnitude) • ex: • distance traveled • temperature • speed limits • Vectors: measure both amount and direction • vector: scalar with a direction • ex: • velocity of a car • weight

  4. Vector or Scalar? Categorize each quantity as being either a vector or a scalar. CategoryQuantity a. ___________________ 5 m b. ___________________ 30 m/s East c. ___________________ 10 mi.North d. ___________________ 20 degrees Celsius e. ___________________ 256 Megabytes f. ___________________ 4000 Calories Scalar Vector Vector Scalar Scalar Scalar

  5. Distance vs. displacement • distance: total miles traveled (scalar) • displacement: change in position (vector) • distance from start to end • 2a. What is the displacement and distance of runners when they finish a one-mile race on an oval track? 1 mi Distance: 0 mi Displacement:

  6. Distance vs. displacement • distance: total miles traveled (scalar) • displacement: change in position (vector) • distance from start to end • 2b. What is your displacement and distance if you walk 3m north and then 5m south? 3m 3m + 5m = 8m Distance: 5m 3m - 5m = 2m south Displacement:

  7. Speed vs. Velocity • Speed ( v ) = distance / time • Velocity ( ) = displacement / time arrows mean they are vectors distance displacement

  8. Time to Practice Go to pg. 248 Complete Problems #3-5 Work ahead! #6-8

  9. Reference Frames • Speed is Relative • R.F. allow you to compare speeds • How fast are you moving now? • Earth is rotating at 1,000 mph

  10. Frame of Reference • Earth is orbiting sun at 66,000 mph • Everything in universe is moving

  11. Frame of Reference • Lets say you are on a train moving 40 mph • If you walk towards the front of the train at 5 mph, you are going 5 mph relative to the train • 1. What is your speed relative to someone standing by the train tracks? 5 mph 40 mph 45 mph

  12. Frame of Reference • Lets say you are on a train moving 40 mph • 2. What is your speed relative to someone standing by the train tracks if you walk towards the back of the train at 5 mph? 5 mph 40 mph 35 mph

  13. Frame of Reference • Is this car moving? • Speed Limit of the Universe: light speed! (3.0 x 108 m/s)

  14. Time to Practice Go to pg. 248

  15. Variable Unit Graphing Rules Distance (m) • Use a ruler (straightedge)! • Label your axes! • (units in parentheses) • time is always the x-axis Time (s)

  16. Distance (m) Time (s) Graphing Rules Distance vs. Time 3.Title the graph! • (Y vs. X)

  17. Graphing Rules 4.SCALE. • Stretch out your axes!

  18. Graphing Rules 5. Use a Pencil!! 6. Do not just connect the dots! Line of best fit curve: smooth line: ruler The line might not touch dots

  19. Distance (m) Time (s) Graphing Rules • Drawing tangent lines • drawn at a point • “balance” ruler on curve • perpendicular with normal Distance vs. Time Ahh. Just right! • make it long enough to find the slope

  20. Graphing: start work! Pg 254

  21. Distance vs. Time (x2, y2) (0.15, y1) Distance (m) Time (s) 0.15 s

  22. Movies And now for a short movie

  23. Eureka: Inertia – 1:25

  24. Eureka: Mass -- broken

  25. Eureka: Speed -- broken

  26. Acceleration • accelerationthe rate of change of velocity • =final velocity • =initial velocity • refers to speeding up and slowing down or… Velocity Speed Direction arrows mean …

  27. ExampleA car moving at 20 m/s comes to a stop in four seconds. What was the car’s acceleration? Given: Unknown:

  28. Examplesolve for acceleration said “negative five meters per second per second” negative acceleration means… slowing down

  29. Acceleration • You “feel” speed when you accelerate • This includes speeding up, slowing down and • sharp turns at constant speed! • All three are accelerations

  30. Eureka: Acceleration I

  31. Eureka: Acceleration II

  32. Start Homework!

  33. Distance vs. Time Graphs Constant speed • Slope • units are • the slope is velocity! Distance (m) Time (s) Distance (m) Time (s) Increasing Speed

  34. Speed vs. Time Graphs • Slope • units are • the slope is acceleration!

  35. Speed vs. Time Graphs speed acceleration Distance traveled

  36. 1. Find the instantaneous acceleration at Points a, b, and c • Points a • Point b • Point c 2 m/s2 (speeding up) 0 (traveling at constant speed) -1 m/s2(slowing down)

  37. 2. Use the graph below to find the velocity from: • start to a • a to b • c to d • What is displacement after 9 sec? x m/s

  38. Freefall • freefall  objects moving under only force of gravity • due to gravity = g • g = 9.8 m/s2 • Terminal velocity is the fastest an object can fall • terminal velocity  when air resistance becomes equal to gravity

  39. Freefall • let’s look at the motion of three objects • An object dropped from rest • An object thrown downwards • An object thrown upwards • All have the sameacceleration! • All of these motions are types of… freefall!

  40. Eureka: Gravity

  41. Lab: Acceleration due to Gravity pg. 270-273 1. Make sure the motion detector only “sees” the ball • Not your 3rd arm or extra head • Not a table or the wire basket • 2. Cover the motion detector with a wire basket • Throw the ball upand catch it 3. Throw the ball after you hear faster beeps

  42. Make sure your graph makes sense • Optional: zoom in on the important stuff Lab: Acceleration due to Gravity pg. 270-273 2. Plot your line of best fit (it should be linear) • 3. Once you are ready to print your graphs: • Plug your LabQuest into the printer • Click File  Print graph • On a Sticky Note write: • your name and # of copies needed • stick it to your 2 graphs 4. Record your data on your data table • Optional: save your data to a USB

  43. Don’t forget to…. READ THE INSTRUCTIONS VERY CAREFULLY. Complete your data table before you erase your data • Label your axis: variable & units • Title your graph: _____ vs. _____

  44. Lab Questions • Displacement, Velocity & acceleration graphs: http://www.youtube.com/watch?v=_ES1JJ7ErzI • Slow Motion Ball: http://www.youtube.com/watch?v=1PyjLXIYMzI&feature=related

  45. Putting it together • Let’s use what we know about graphs to make two more formulas. • Let’s look at the graph from ti to tf

  46. Putting it together • Each time matches up with a velocity • Initial velocity is vi • final velocity is vf vf vi

  47. Putting it together • To find distance: • area between the line and the x-axis • d = area of rectangle + area of triangle vf vi

  48. Putting it together • d = area of rectangle + area of triangle • area of rectangle = • area of triangle = vf vi

  49. Putting it together we now have a connection between a and d

  50. Putting it together • solve for t from first a equation • substitute into second a equation • a little fancy algebra and… nice if you do not have t

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