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Scalars: Distance and Speed

Scalars: Distance and Speed. SPH3U. Scalars: Learning Goals. The student will be able to provide examples of scalar quantities relating to motion. (B3.2) The student will be able to solve problems relating to distance using algebraic representations. (B2.5)

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Scalars: Distance and Speed

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  1. Scalars: Distance and Speed SPH3U

  2. Scalars: Learning Goals • The student will be able to provide examples of scalar quantities relating to motion. (B3.2) • The student will be able to solve problems relating to distance using algebraic representations. (B2.5) • Vocabulary: scalar, distance, average speed, instantaneous speed

  3. Scalars A scalar quantity has magnitude (size) only.

  4. Scalars A scalar quantity has magnitude (size) only. e.g. time is a scalar quantity.

  5. Scalars A scalar quantity has magnitude (size) only. e.g. time is a scalar quantity. Note that magnitude includes units!!!

  6. Examples of scalars: distance Scalars

  7. Examples of scalars: distance speed Scalars

  8. Examples of scalars: distance speed time and frequency Scalars

  9. Examples of scalars: distance speed time and frequency work, potential and kinetic energy Scalars

  10. Examples of scalars: distance speed time and frequency work, potential and kinetic energy voltage, current, and resistance etc. Scalars

  11. Adding Scalars: Example Ms. Rosebery walks 2 m [North] and 1 m [South]. What is the total distance she walks?

  12. Adding Scalars: Example Ms. Rosebery walks 2 m [North] and 1 m [South]. What is the total distance she walks? 2 m + 1 m = 3 m Distance is a scalar: direction doesn’t matter.

  13. Average Speed Average speed is defined as the distance travelled per interval of time, or

  14. Average Speed Average speed is defined as the distance travelled per interval of time, or

  15. Average Speed Average speed is defined as the distance travelled per interval of time, or Speed therefore has units of distance over time or m/s.

  16. Average Speed Average speed is defined as the distance travelled per interval of time, or Speed therefore has units of distance over time or m/s. (And, like distance, is a scalar.)

  17. Finding Speed: An Example Matt runs 180 m in 0.75 min. What is his average speed in m/s?

  18. Finding Speed: An Example Matt runs 180 m in 0.75 min. What is his average speed in m/s?

  19. Finding Speed: An Example Matt runs 180 m in 0.75 min. What is his average speed in m/s?

  20. Finding Speed: An Example Matt runs 180 m in 0.75 min. What is his average speed in m/s?

  21. Finding Speed: An Example Matt runs 180 m in 0.75 min. What is his average speed in m/s?

  22. Finding Distance and Time The equation for average speed can be rearranged to solve for distance or time:

  23. Finding Distance and Time The equation for average speed can be rearranged to solve for distance or time: solved for distance solved for time

  24. Giving Distances in Units of Time Often we (incorrectly, to physicists), give distances in units of time. For example, “How far is it to McMaster?” “10 minutes.”

  25. Giving Distances in Units of Time Often we (incorrectly, to physicists), give distances in units of time. For example, “How far is it to McMaster?” “10 minutes.” When we do this, we are making assumptions about the speed at which we will be travelling (we are taking our vavg as a given, and if we know Dd and vavg, we also know Dt).

  26. “How far” is Megan’s run? If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  27. “How far” is Megan’s run? If Megan is running at 4 m/s, how long will it take her to run a 5 km trail? or 20 minutes

  28. Average vs. Instantaneous We can assume that Megan was running at a constant 4 m/s, but was Matt running at a constant 4.0 m/s?

  29. Average vs. Instantaneous We can assume that Megan was running at a constant 4 m/s, but was Matt running at a constant 4.0 m/s? Not necessarily. His instantaneous speed at any instant may have been different from his average speed (e.g., it may have been zero at the start of his run).

  30. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (a) instantaneous speed at the first 1.0-km mark? (b) average speed for the entire walk?

  31. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (a) instantaneous speed at the first 1.0-km mark?

  32. Average vs. Instantaneous Ms. Rosebery walked 2.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (a) instantaneous speed at the first 1.0-km mark? She’s still walking the first 3.0 km, so she’s walking at 1.5 m/s.

  33. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (b) average speed for the entire walk?

  34. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (b) average speed for the entire walk? It’s not 1.25 m/s. We consider total time and total distance when calculating vavg.

  35. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (b) average speed for the entire walk?

  36. Average vs. Instantaneous Ms. Rosebery walked 3.0 km at a constant speed of 1.5 m/s and another 1.0 km at a constant speed of 1.0 m/s. What was her: (b) average speed for the entire walk?

  37. More Practice Homework: Scalars: Distance and Speed

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