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Linear Motion

Linear Motion. Fast. speed depends on distance and time average speed uses total distance and total time. Frame of Reference. speed is relative FOR is something to compare speed to How fast are you moving now? Earth is rotating at 1,000 mph. Frame of Reference.

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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

  3. Frame of Reference • speed is relative • FOR is something to compare speed to • How fast are you moving now? • Earth is rotating at 1,000 mph

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

  5. Frame of Reference • So, if you drive 55 mph, you are going 55mph relative to the earth • Universe speed limit:speed of light • 3 x 10 8m/s • Is car moving?

  6. Velocity • Scalar vs. Vector • scalar: measures only the amount • ex: temperature, area, distance traveled • vector: measures both amount and direction • vector: scalar and direction • ex: weight • in whichdirection is weight directed?

  7. Displacement • speed = distance / time • velocity = displacement / time • distance: log of total miles traveled • displacement: change in position • displacement: distance from start to end arrows mean they are vectors distance displacement

  8. Time to Practice Go to pg. 295

  9. Variable Unit Graphing Rules Distance (m) • Use a ruler (straightedge)! • Label your axes! • (units in parentheses) • time is always below Time (s)

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

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

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

  13. 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

  14. Graphing

  15. Movies And now for a short movie

  16. Eureka: Inertia

  17. Eureka: Mass

  18. Eureka: Speed

  19. Labette Graphing Motion pg. 305

  20. Acceleration • accelerationthe rate of change of velocity • final velocity • initial velocity • refers to speeding up and slowing down or… arrows mean …

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

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

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

  24. Eureka: Acceleration I

  25. Speed vs. Time Graphs • look at the slope • units are m/s/s=m/s2 • acceleration! • same answer as example

  26. Speed vs. Time Graphs • So, to summarize the graphs: • For distance vs. time: • slope = speed • For speed vs. time: • slope = acceleration • area under line = distance covered

  27. Eureka: Acceleration II

  28. Freefall • freefall objects moving under only force of gravity • terminal velocity when air resistance becomes equal to gravity • due to gravity = g • g = 9.8 m/s2

  29. Freefall • let’s look at the motion of three objects • one dropped from rest • one thrown downwards • one thrown upwards • All of these motions are types of… freefall!

  30. Freefall • let’s look at the motion of three objects • one dropped from rest • one thrown downwards • one thrown upwards • All of these motions are types of… freefall!

  31. Eureka: Gravity

  32. Lab Acceleration due to Gravity pg. 314

  33. 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

  34. Putting it together • each time matches up with a velocity • First velocity is vi and last is vf vf vi

  35. Putting it together • To find distance: • area under the line • two shapes: • triangle • and rectangle vf vi

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

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

  38. 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

  39. Putting it together • use equation 1 only if acceleration is zero • use equations 2-4 only if constant acceleration

  40. Putting it together • notice there are no arrows • they are still all vectors

  41. Putting it together • vectors mean that direction is important • ex. positive for up, negative for down

  42. ExampleA spear is thrown down at 15 m/s from the top of a bridge at a fish swimming along the surface below. If the bridge is 55 m above the water, how long does the fish have before it gets stuck? Given: why negative? Want:

  43. Example Which equation has vi, d, a and t? • Eqn 3 works, but…you would need quadratic (bleh!) • Eqn 2 would work if we had vf. Eqn 4 can get us vf!

  44. Example First, eqn. 4 positive or negative?

  45. Example • solve for t in eqn 2. • substitute vf into eqn 2.

  46. Check Yourself Turn to pg. 321

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