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Linear Motion

This guide explores the concepts of linear motion, focusing on speed and velocity. Learn how average speed combines total distance and time, and differentiate between scalars and vectors. Scalars measure magnitude, such as distance and temperature, while vectors encompass direction, as seen in velocity and weight. Additionally, we discuss distance vs. displacement, introduce frames of reference, and outline the principles of acceleration. Gain insights into interpreting graphs related to motion, and practice problems to reinforce these fundamental physics concepts.

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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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