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More Practice: Distance, Speed, and Unit Conversion

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Vectors: Displacement and Velocity: Learning Goals The student will be able to distinguish between distance and displacement and speed and velocity. (B2.1) The student will be able to distinguish between distance and displacement and speed and velocity. (B2.1) The student will be able to distinguish between constant, instantaneous, and average speed and give examples of each involving uniform and non-uniform motion. (B3.1) The student will be able to distinguish between constant, instantaneous, and average speed and give examples of each involving uniform and non-uniform motion. (B3.1)

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Vectors: Displacement and Velocity SPH4C

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Vectors A vector quantity has both magnitude and

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Vectors A vector quantity has both magnitude and direction.

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Vectors The direction is given in square brackets after the units:

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Vectors A vector quantity has both magnitude and direction. The direction is given in square brackets after the units: e.g., 5 km [West]

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Vectors Examples of vectors: displacement velocity

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Vectors Examples of vectors: displacement velocity acceleration

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Vectors Examples of vectors: displacement velocity acceleration force etc.

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Displacement Displacement is how far an object is from its starting position and is not simply distance travelled + a direction.

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Displacement E.g., the distance travelled here by a driver commuting from Manhattan to N.J. was 14.5 km even though the displacement was only 2.7 km [North].

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Displacement Example: Ms. Rosebery walks 2 m [East] and then 1 m [West]. What was her distance travelled? What was her displacement?

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Displacement Example: Ms. Rosebery walks 2 m [East] and then 1 m [West]. What was her distance travelled? What was her displacement? Distance travelled: d = 2 m + 1 m = 3 m

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Displacement Example: Ms. Rosebery walks 2 m [East] and then 1 m [West]. What was her distance travelled? What was her displacement? Distance travelled: d = 2 m + 1 m = 3 m Displacement: 2 m 1 m

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Displacement Example: Ms. Rosebery walks 2 m [East] and then 1 m [West]. What was her distance travelled? What was her displacement? Distance travelled: d = 2 m + 1 m = 3 m Displacement: She is 1 m [East] of her original starting position. 2 m 1 m

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Displacement We can represent [East] as the positive direction and [West] as the negative direction: 2 m 1 m

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Displacement We can represent [East] as the positive direction and [West] as the negative direction: = 2 m [East] + 1 m [West] = + 2 m – 1 m 2 m 1 m

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Displacement We can represent [East] as the positive direction and [West] as the negative direction: = 2 m [East] + 1 m [West] = + 2 m – 1 m = + 1 m 2 m 1 m

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Displacement We can represent [East] as the positive direction and [West] as the negative direction: = 2 m [East] + 1 m [West] = + 2 m – 1 m = + 1 m = 1 m [East] 2 m 1 m

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Directions It is conventional to represent the following directions as positive: forward forward

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Directions It is conventional to represent the following directions as positive: forward forward right right

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Directions It is conventional to represent the following directions as positive: forward forward right right up up

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Directions It is conventional to represent the following directions as positive: forward forward right right up up North North East East

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Velocity Velocity is similarly not simply speed + a direction.

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Velocity

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Velocity

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Velocity Example: Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. What was her average speed? What was her average velocity?

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Velocity Example: Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. What was her average speed? What was her average velocity?

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Velocity Example: Ms. Rosebery walks 2 m [East] and then 1 m [West] in 3 s. What was her average speed? What was her average velocity?

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Instantaneous Velocity Average velocity is rarely calculated for an object changing direction. It makes more sense to talk about the instantaneous velocity, which is the speed + the direction at that particular instant.

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Instantaneous Velocity Average velocity is rarely calculated for an object changing direction. It makes more sense to talk about the instantaneous velocity, which is the speed + the direction at that particular instant.

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Instantaneous Velocity Assuming Ms. Rosebery walked at constant speed, what was her instantaneous velocity at: 1.5 s? 2 s? 2.5 s?

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Instantaneous Velocity Assuming Ms. Rosebery walked at constant speed, what was her instantaneous velocity at: 1.5 s?1 m/s [East] 2 s? 2.5 s?

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Instantaneous Velocity Assuming Ms. Rosebery walked at constant speed, what was her instantaneous velocity at: 1.5 s?1 m/s [East] 2 s?0 m/s (while she is changing direction) 2.5 s?1 m/s [West]

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Instantaneous Velocity Assuming Ms. Rosebery walked at constant speed, what was her instantaneous velocity at: 1.5 s?1 m/s [East] 2 s?0 m/s (while she is changing direction) 2.5 s?

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More Practice More Practice: Displacement and Velocity and Graphing Motion

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