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A Summary of Motion

A Summary of Motion. Measurements, Graphs and Equations. Scalars and Vectors. Scalar quantities are measurements that have no statement of direction. Vector quantities are measurements that have a statement of direction.

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A Summary of Motion

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  1. A Summary of Motion Measurements, Graphs and Equations

  2. Scalars and Vectors • Scalar quantities are measurements that have no statement of direction. • Vector quantities are measurements that have a statement of direction. • Direction can be forward or backwards, indicated by + or - , or it can be compass points such as N, S, E, or W. Up and down are also directions

  3. Position • Position is the location of an object based on a reference point. Often, though not always, the reference point is assigned a zero value. • A reference point does not have to be zero, it can be any point the author of a problem decides it should be. • The starting point in a motion problem does not have to be the reference point.

  4. Displacement • Displacement is a measure of an object’s change in position. • Displacement is usually measured in a straight line from the start position to the end position of the motion. • Displacement has a direction associated with it. This could be forward vs reverse, or north vs south, or east vs west, or up vs down.

  5. Speed • Speed is a statement about how fast an object is traveling. • Speed measures the rate of change between distance and time. • Speed has no statement of direction. • Speed is found by dividing the total distance traveled by an object by the time interval during which the object moved. • Speed is the magnitude of an object’s velocity • Speed has a number and a unit; i.e. 5 m/s

  6. Velocity • Velocity is a statement about how fast an object is going plus the direction it is going. • Velocity measures the rate of change between displacement and time. • Velocity has a statement of direction. • Velocity is found by dividing the displacement of an object by the time interval during which the object moved. • Velocity’s magnitude is speed • Velocity has a number, a unit, and direction; i.e. 5 m/s, E

  7. Acceleration • Acceleration is a statement about how fast an object’s velocity changes. • Acceleration measures the rate of change between velocity and time. • Acceleration has a statement of direction. • Acceleration is found by dividing the change in velocity of an object by the time interval during which the velocity changed. • Acceleration has a number, a unit, and direction; i.e. 9.8 m/s^2, N

  8. Constant velocity (uniform motion) • Constant velocity is a situation where an object moves along with a constant change in its position. • On the right you’ll see a typical position-time graph where the velocity is constant. Position vs Time

  9. Constant Velocity (uniform motion) • Constant velocity is a situation where an object moves along with a constant change in its position. • On the right you’ll see a typical velocity-time graph where the velocity is constant Velocity vs Time

  10. Uniform (constant) Acceleration • Uniform or constant acceleration is a situation where an object moves along with a constant change in its velocity. • On the right you’ll see a typical position-time graph where the acceleration is constant Position vs Time

  11. Uniform (constant) Acceleration • Uniform or constant acceleration is a situation where an object moves along with a constant change in its velocity. • On the right you’ll see a typical velocity-time graph where the acceleration is constant Velocity vs Time

  12. Falling Bodies and Acceleration • According to the Law of Gravity, all objects fall with the same rate of acceleration when they are in free fall. • Free fall is a situation where air friction has no effect on the falling body. • On earth (only) the average rate of downwards acceleration g is 9.8 m/s^2

  13. Summary: • We have looked at three generic scenarios. • 1. Constant velocity • 2. Acceleration in a horizontal direction • 3. Acceleration in a vertical direction; free fall • For further review it is strongly recommended that you go to your text references and read, study, and take notes on the example and the practice problems in your textbook.

  14. Acceleration due to Gravity • Uniform acceleration of gravity is a situation where an object falls along with a constant change in its velocity. • On the right you’ll see a typical position-time graph where an object accelerates downwards. Position vs Time

  15. Acceleration due to Gravity • Uniform acceleration of gravity is a situation where an object falls along with a constant change in its velocity • On the right you’ll see a typical velocity-time graph where an object accelerates downwards. Velocity vs Time

  16. Time; clock time and time interval • Time can be thought of in one of two ways. It can be an “exact time” as in “What time is it right now?” or it can represent a period of time often referred to as the duration of an event. • t or Clock time is what it says on a clock, etc. • /\t = t(f) – t(i) is the difference between two clock times and is often referred to as the duration of an event.

  17. Distance and Speed • Distance or what is often called total distance is not the same as displacement. It is simply the total of all of the distances an object travels in a time interval • Speed is simply equal to the total of all of the distances divided by the time interval. • Equation: Speed = d(total) / /\t

  18. Equations for Constant velocity • Constant velocity: velocity that remains the same during the time interval an oject’s motion is being studied or observed. • /\d = d(f) – d(i); often d(i) = 0 m, km, mi, etc., so /\d is simply d(f) or d(total) • V(ave) = /\d / /\t • /\d = V(ave) * /\t • /\t = /\d / V(ave)

  19. Equations for Uniform Acceleration • Uniform acceleration: The situation where the velocity continuously changes by the same amount of velocity each second, thus causing position to change by an ever increasing amounts per unit of time (i.e. per second) • a(ave) = /\v / /\t; where /\v = v(f) – v(i) • d(f) = d(i) + 0.5 [{vi + vf} / 2] /\t • d(f) = v(i) /\t + 0.5 a /\t^2 • v(f) = v(i) + a t • v(f)^2 = v(i)^2 + 2 a /\d

  20. Equations for Uniform Acceleration during free fall. (g = a = 9.8 m/s^2) • Uniform acceleration: The situation where the velocity continuously changes by the same amount of velocity each second, thus causing position to change by an ever increasing amounts per unit of time (i.e. per second) • g(ave) = /\v / /\t; where /\v = v(f) – v(i) • d(f) = d(i) + 0.5 [{v(i) + v(f)} / 2] /\t • d(f) = v(i) /\t + 0.5 g /\t^2 • v(f) = v(i) + g /\t • vf^2 = vi^2 + 2 g /\d

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