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Answers to More Practice with GUSS

Explore scalar quantities, average speed calculations, unit conversions, and solving for distance and time relationships. Learn essential concepts to excel in physics and quantitative data analysis.

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Answers to More Practice with GUSS

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  1. Answers to More Practice with GUSS

  2. Answers to More Practice with GUSS

  3. Answers to More Practice with GUSS

  4. Answers to More Practice with GUSS

  5. Answers to More Practice with GUSS

  6. Answers to More Practice with GUSS

  7. Answers to More Practice with GUSS

  8. Answers to More Practice with GUSS

  9. Answers to More Practice with GUSS

  10. Distance, Speed and Unit Conversions: Learning Goals • The student will be able to solve simple problems involving one-dimensional average speed, distance, and elapsed time, using algebraic equations (B.2.6) • The student will be able to use and convert between different numeric representations of quantitative data. (A1.12)

  11. SPH4C Distance, Speed and Unit Conversions

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

  13. Scalars A scalar quantity has magnitude (size) only. Examples of scalars: • distance

  14. Scalars A scalar quantity has magnitude (size) only. Examples of scalars: • distance • speed

  15. Scalars A scalar quantity has magnitude (size) only. Examples of scalars: • distance • speed • time

  16. Scalars A scalar quantity has magnitude (size) only. Examples of scalars: • distance • speed • time • work, potential and kinetic energy

  17. Scalars A scalar quantity has magnitude (size) only. Examples of scalars: • distance • speed • time • work, potential and kinetic energy • voltage, current, and resistance • etc.

  18. Adding Scalars: Example Alex walks 2 m [North] and 1 m [South]. What is the total distance he walks?

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

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

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

  22. Average Speed Average speed is defined as the distance travelled per interval of time, or Speed will therefore have units of distance over time (typically m/s).

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

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

  25. Unit conversion But what is 0.75 minutes in seconds?

  26. Unit conversion But what is 0.75 minutes in seconds? To express a measurement in different units, we multiply the measurement by a conversion factor that is equal to 1.

  27. Unit Conversions Since 1 minute = 60 seconds, The unit we want to cancel out goes in the denominator of the factor. The unit we want to get goes in the numerator.

  28. Unit Conversions The unit we want to cancel out goes in the denominator of the factor. The unit we want to get goes in the numerator.

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

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

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

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

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

  34. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  35. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  36. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  37. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail? ? Does it make sense that it takes someone 1.25 s to run 5 km?

  38. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  39. Another Example If Megan is running at 4 m/s, how long will it take her to run a 5 km trail?

  40. Watch for those prefixes! A metric prefix may be used to indicate a unit that is some power of ten larger or smaller than the base unit.

  41. Watch for those prefixes! A metric prefix may be used to indicate a unit that is some power of ten larger or smaller than the base unit. For example, 1 km =

  42. Watch for those prefixes! A metric prefix may be used to indicate a unit that is some power of ten larger or smaller than the base unit. For example, 1 km = 1000 m or 1 × 103 m

  43. All the Prefixes

  44. Common Prefixes For example, • 2 ms =

  45. Common Prefixes For example, • 2 ms = 2 × 10-6 s Know how to enter this number in your calculator : (usually as either 2 EXP -6 or 2 EE -6 or 2 10x -6).

  46. Common Prefixes For example, • 2 ms = 2 × 10-6 s • 2 ns =

  47. Common Prefixes For example, • 2 ms = 2 × 10-6 s • 2 ns = 2 × 10-9 s

  48. Common Prefixes For example, • 2 ms = 2 × 10-6 s • 2 ns = 2 × 10-9 s • 20 ns =

  49. Common Prefixes For example, • 2 ms = 2 × 10-6 s • 2 ns = 2 × 10-9 s • 20 ns = 20 × 10-9 s

  50. Multiple Conversion Factors Finally, converting some units may require multiplying by more than one conversion factor.

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