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Ch. 3 & 4 Vectors, Speed, Velocity, & Acceleration

Ch. 3 & 4 Vectors, Speed, Velocity, & Acceleration. What is the difference between distance and position?. Engaging with the concept. Distance is always positive. It doesn’t tell you where you are because it has no direction information.

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Ch. 3 & 4 Vectors, Speed, Velocity, & Acceleration

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  1. Ch. 3 & 4Vectors, Speed, Velocity, & Acceleration

  2. What is the difference between distance and position? Engaging with the concept Distance is always positive. It doesn’t tell you where you are because it has no direction information. Displacement is a change in position that includes direction.

  3. Position Position tells you where you are relative to an origin. Positive and negative values tell you whether you are in front or behind, or to the left or right of the origin.

  4. Displacement Displacement is a change in position. Positive and negative values indicate direction.

  5. Displacement is a vector Displacement is a vector because it contains direction information. For motion along a line, direction is positive or negative.

  6. Some quantities in physics include direction information. Can you name any? Any variable in which it makes a difference which direction you go, such as forward or backward, must be a vector. What is a vector?

  7. Distance is a scalar Distance is a scalar quantity. It does not include direction information.

  8. Scalars Mass and temperature are scalars because you don’t need a “direction” to understand what their values mean. What is a scalar?

  9. Adding displacements An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? Add displacements graphically by drawing vectors to scale: • The first vector starts at the initial position. • The second vector starts at the end of the first vector.

  10. Adding displacements An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? You can also use numerical addition. This is faster and more accurate.

  11. Identify each variable listed below as either a vector or a scalar. Are there any variables that are neither vectors nor scalars? Assessment • weight • force • displacement • length • velocity • Time

  12. Identify each variable listed below as either a vector or a scalar. Are there any variables that are neither vectors nor scalars? Assessment • weight vector • force vector • displacement vector • length scalar • velocity vector • time scalar All variables used in this course are either vectors or scalars.

  13. A boat travels 5 kilometers east, then 8 kilometers north, and then 8 kilometers west. • How would you calculate the boat’s displacement? • How would you calculate the boat’s distance? Assessment (-8, 0) km (0, 8) km (5, 0) km

  14. Speed versus velocity Are speed and velocity just two different words for the same thing? • In everyday life you probably use the words speed and velocity interchangeably. • In physics class, speed and velocity are related, but not exactly the same.

  15. s The speed is the distance traveled divided by the time taken. speed is always positive! The velocity is the change in position divided (displacement) by the change in time. Moving forward is a positive velocity.Moving backward is a negative velocity. Equations

  16. Brainstorm: An accelerating object has a changing velocity. Can you share an example of something accelerating?

  17. Examples a coaster making a turn a ball rolling uphill a baseball falling

  18. What is acceleration? 4 m/s 4 m/s 4 m/s 4 m/s • Two balls are moving to the right. Their velocity at each second is shown. • Which ball is accelerating? • What is its acceleration? Ball 1 0 m/s 4 m/s 2 m/s Ball 2 6 m/s

  19. What is acceleration? 4 m/s 4 m/s 4 m/s 4 m/s • Two balls are moving to the right. Their velocity at each second is shown. • Which ball is accelerating? • What is its acceleration? • Ball 2 is accelerating at +2 m/s per second: • a= +2 m/s2 Ball 1 0 m/s 4 m/s 2 m/s Ball 2 6 m/s

  20. The meaning of acceleration Acceleration is the rate at which velocity changes. a = acceleration (m/s2) Δv = change in velocity (m/s) Δt = change in time (s)

  21. Units of acceleration The acceleration tells you how many meters per second your velocity changes in each second. These units are usually written as meters per second squared.

  22. What is free fall? An object is in free fall whenever it moves solely under the influence of gravity, regardless of its direction. A ball thrown up, with negligible air resistance A ball launched at ANY angle, as long as there is negligible air resistance A ball falling down, with negligible air resistance

  23. Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9.8 m/s2. If an object is dropped from rest, then . . . • after 1 second its velocity is -9.8 m/s. • after 2 seconds its velocity is -19.6 m/s. • after 3 seconds its velocity is __?___ • after 10 seconds its velocity is __?___

  24. Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9.8 m/s2. If an object is dropped from rest, then . . . • after 1 second its velocity is -9.8 m/s. • after 2 seconds its velocity is -19.6 m/s. • after 3 seconds its velocity is -29.4 m/s. • after 10 seconds its velocity is -98 m/s.

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