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One Dimensional Motion

One Dimensional Motion. Frames of Reference Distance and Displacement Speed and Velocity Graphical Relations. Motion may seem simple enough, but physics is able to make it more complicated then you could imagine Our first topic will be motion in one dimension

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One Dimensional Motion

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  1. One Dimensional Motion Frames of Reference Distance and Displacement Speed and Velocity Graphical Relations

  2. Motion may seem simple enough, but physics is able to make it more complicated then you could imagine • Our first topic will be motion in one dimension • That includes motion along a straight line either going left and right or up and down Kinematics: Motion in Physics

  3. Watch my movements carefully … A lesson in observation…

  4. Watch my movements carefully … • Keep watching … A lesson in observation…

  5. Watch my movements carefully … • Keep watching … • Keep watching … A lesson in observation…

  6. Watch my movements carefully … • Keep watching … • Keep watching … • How much did I move? • ~1 cm? • ~1 m? • ~1 km? A lesson in observation…

  7. If I had to estimate I would say in the past 8 seconds I moved approximately 10,000 km • If you missed it you must not be paying close enough attention or maybe you blink too long A lesson in observation…

  8. Frames of Reference

  9. Frames of Reference

  10. It would be much too complicated and tedious to consider all these other motions so we choose a frame of reference for motion that ignores those • You can usually choose your frame of reference so that the starting point is the origin and it makes problems slightly easier Frames of Reference

  11. I want the right half of the room to close your eyes until I tell you to open them • I want the left half of the room to keep your eyes open and pay attention to my motion • Ready … More strange observations…

  12. Right half of the room, how much did I move? • Left half of the room, how much did I move? • In Physics we need a way to differentiate between what the right side of the room saw and the left side of the room Motion

  13. We have two terms to describe an object’s movement • Distance: the actual length traveled by an object regardless of direction • Displacement: the difference between an objects final position and initial position • Δx = xf - xi • Notice that displacement can be negative or positive Distance versus Displacement

  14. Coach Seabolt makes the soccer players run the field (~100 meters long) 7 times. • What is the distance traveled by a player? • What is the displacement of a player? Simple Example

  15. The ground moves 8 cm in a certain region. What happened? Is displacement all we need to know?

  16. Earthquake?

  17. Continental Drift?

  18. The time it takes for the displacement to happen is just as important as the change in position Something else is important in motion

  19. Velocity: the displacement of an object divided by the time in which the displacement occurs • Velocity = Δx/Δt (CAN ONLY BE USED WHEN VELOCITY IS CONSTANT!) • Just like displacement can be negative, velocity can also be negative • How do we decide if velocity is negative or positive? Calculating Velocity

  20. Speed • Have you ever seen a car that has negative numbers on the speedometer? • That’s because a car doesn’t care about the direction only how fast • Speed: the distance traveled divided by the time • Speed = distance/time

  21. Instantaneous • The value of a physical variable at a particular moment or instant • Average • The value of a physical variable over a given period of time Instantaneous versus Average

  22. How are displacement and velocity related graphically? • Given a graph of position versus time, how can you determine the velocity and vice versa? • Let’s look at a simple example …

  23. Displacement -> Velocity • The motion of a car is represented in the graph to the right. • Rank the velocity of the car at the four points given. • How did you know this?

  24. The velocity of an object is equal to the slope of the displacement versus time graph! • Average Velocity – Slope between two points • Instantaneous Velocity – Slope along a line containing the point • In fact, anytime you want to divide two variables on a graph, take the slope! Displacement -> Velocity

  25. The two graphs to the right represent the velocity of two cars. • Which car traveled further, car A or Car B? Velocity -> Displacement

  26. The displacement of an object is equal to the area of the velocity versus time graph between the graph and the x-axis! • In fact, anytime you want to multiply two variables on a graph, find the area between the curve and the x-axis! Velocity -> Displacement

  27. Consider the following: • I slow down from 20 m/s to 0 m/s • What just happened? So is displacement and velocity all we need to know?

  28. I slowly stop for a red light

  29. I slam on my brakes for a deer

  30. The time it takes to change from your initial velocity to your final velocity is also important Something else is important other than change in velocity

  31. Acceleration

  32. As always it is important to understand what the units are using dimensional analysis: • Try to determine the units of acceleration given the following formula: • Acceleration = Δvelocity Δtime Acceleration = meters/second second Acceleration = meters = m second2 s2 What are the units of acceleration?

  33. A car traveling at 7 m/s accelerates at 2.5 m/s2 to reach a speed 17 m/s. How long does the acceleration take? • With an acceleration of -1.2 m/s2 how long will it take a bike to stop if it is initially moving at 6.5 m/s? • Problem 1: 4 seconds • Problem 2: ~5.4 seconds Try these simple examples…

  34. Remember, positive and negative signs ONLY indicate DIRECTION! • With this in mind, determine what happens given the following: Positive and Negative Acceleration

  35. What does negative or positive acceleration mean? • Imagine two cars traveling down a highway in opposite directions. What is the sign of the velocity of each of the cars?

  36. Assume that we are going to give each car a positive acceleration. • The question of the day is what direction would a positive acceleration be pointing? Lets accelerate the cars…

  37. Positive acceleration is to the north! • Notice the direction of the velocity compared to the direction of the acceleration. Acceleration does not mean speeding up!!! It just means a change in velocity!!! Which car has a decreasing velocity?

  38. Positive acceleration is to the north! • Car 1 is increasing its velocity and Car 2 is decreasing its velocity. Sound confusing? It shouldn’t be, at least if you pay attention to the direction of the arrows!

  39. Instead of giving it a positive acceleration, let’s give the cars a negative acceleration • Remember that a negative acceleration does not mean you are slowing down, the negative is only telling you the direction! Let’s look at the other direction…

  40. Negative acceleration is south! • This time Car 2 has an increasing velocity while Car 1 has a decreasing velocity. Don’t forget the negative sign just tells you direction, it doesn’t mean slowing down!!!

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