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Kinematics: Motion in One Dimension

Kinematics: Motion in One Dimension. 2.1 Displacement & Velocity Learning Objectives. Describe motion in terms of displacement, time, and velocity Calculate the displacement of an object traveling at a known velocity for a specific time interval

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Kinematics: Motion in One Dimension

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  1. Kinematics:Motion in One Dimension

  2. 2.1 Displacement & VelocityLearning Objectives • Describe motion in terms of displacement, time, and velocity • Calculate the displacement of an object traveling at a known velocity for a specific time interval • Construct and interpret graphs of position versus time

  3. Essential Concepts • Frames of reference • Vector vs. scalar quantities • Displacement • Velocity • Average velocity • Instantaneous velocity • Acceleration • Graphical representation of motion

  4. Reference Frames • Motion is relative • When we say an object is moving, we mean it is moving relative to something else (reference frame)

  5. Scalar Quantities & Vector Quantities • Scalar quantities have magnitude • Example: speed 15 m/s • Vector quantities have magnitude and direction • Example: velocity 15 m/s North

  6. Displacement • Displacement is a vector quantity • Indicates change in location (position) of a body ∆x = xf - xi • It is specified by a magnitude and a direction. • Is independent of the path traveled by an object.

  7. Displacement is change in position www.cnx.org

  8. Displacement vs. Distance • Distance is the length of the path that an object travels • Displacement is the change in position of an object

  9. Describing Motion Describing motion requires a frame of reference http://www.sfu.ca/phys/100/lectures/lecture5/lecture5.html

  10. Determining Displacement In these examples, position is determined with respect to the origin, displacement wrt x1 http://www.sfu.ca/phys/100/lectures/lecture5/lecture5.html

  11. Indicating Direction of Displacement Direction can be indicated by sign, degrees, or geographical directions.

  12. Displacement • Linear change in position of an object • Is not the same as distance

  13. Displacement • Distance = length (blue) • How many units did the object move? • Displacement = change in position (red) • How could you calculate the magnitude of line AB? • ≈ 5.1 units, NE

  14. Reference Frames & Displacement • Direction is relative to the initial position, x1 • x1 is the reference point

  15. Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information:

  16. Average Velocity

  17. Velocity • Example • A squirrel runs in a straight line, westerly direction from one tree to another, covering 55 meters in 32 seconds. Calculate the squirrel’s average velocity • vavg = ∆x / ∆t • vavg = 55 m / 32 s • vavg = 1.7 m/s west

  18. Velocity can be represented graphically: Position Time Graphs

  19. Velocity can be interpreted graphically: Position Time Graphs Find the average velocity between t = 3 min to t = 8 min

  20. Calculate the average velocity for the entire trip

  21. Formative Assessment:Position-Time Graphs Object at rest? Traveling slowly in a positive direction? Traveling in a negative direction? Traveling quickly in a positive direction? dev.physicslab.org

  22. Average vs. Instantaneous Velocity • Velocity at any given moment in time or at a specific point in the object’s path

  23. Position-time when velocity is not constant

  24. Average velocity compared to instantaneous velocity Instantaneous velocity is the slope of the tangent line at any particular point in time.

  25. Instantaneous Velocity • The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short.

  26. 2.2 Acceleration

  27. 2.2 AccelerationLearning Objectives • Describe motion in terms of changing velocity • Compare graphical representations of accelerated and non-accelerated motions • Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration

  28. X-t graph when velocity is changing

  29. Acceleration Acceleration is the rate of change of velocity.

  30. Acceleration: Change in Velocity • Acceleration is the rate of change of velocity • a = ∆v/∆t • a = (vf – vi) / (tf – ti) • Since velocity is a vector quantity, velocity can change in magnitude or direction • Acceleration occurs whenever there is a change in magnitude or direction of movement.

  31. Acceleration Because acceleration is a vector, it must have direction Here is an example of negative acceleration:

  32. Customary Dimensions of Acceleration • a = ∆v/∆t • = m/s/s • = m/s2 • Sample problems 2B A bus traveling at 9.0 m/s slows down with an average acceleration of -1.8 m/s. How long does it take to come to a stop?

  33. Negative Acceleration • Both velocity & acceleration can have (+) and (-) values • Negative acceleration does not always mean an object is slowing down

  34. Is an object speeding up or slowing down? • Depends upon the signs of both velocity and acceleration • Construct statement summarizing this table.

  35. Velocity-Time Graphs • Is this object accelerating? • How do you know? • What can you say about its motion? www.gcsescience.com

  36. Velocity-Time Graph • Is this object accelerating? • How do you know? • What can you say about its motion? • What feature of the graph represents acceleration? www.gcsescience.com

  37. Velocity-Time Graph dev.physicslab.org

  38. Displacement with Constant Acceleration (C)

  39. Displacement on v-t Graphs How can you find displacement on the v-t graph?

  40. Displacement on v-t Graphs Displacement is the area under the line!

  41. Graphical Representation of Displacement during Constant Acceleration

  42. Displacement on a Non-linear v-t graph • If displacement is the area under the v-t graph, how would you determine this area?

  43. Final velocity of an accelerating object

  44. Displacement During Constant Acceleration (D)

  45. Graphical Representation

  46. Derivation of the Equation

  47. Final velocity after any displacement (E) A baby sitter pushes a stroller from rest, accelerating at 0.500 m/s2. Find the velocity after the stroller travels 4.75m. (p. 57) Identify the variables. Solve for the unknown. Substitute and solve.

  48. Kinematic Equations

  49. 2.3 Falling Objects Objectives • Relate the motion of a freely falling body to motion with constant acceleration. • Calculate displacement, velocity, and time at various points in the motion of a freely falling object. • Compare the motions of different objects in free fall.

  50. Motion Graphs of Free Fall v-t graph x-t graph

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