1. SKUBIS © 2003 Graphical Analysis of Motion

2. SKUBIS © 2003 <92 Two is less than nine Familiar Mathematical Relationships Less than

3. SKUBIS © 2003  9.81m/s 2 g Gravity on earth Familiar Mathematical Relationships Equals

4. SKUBIS © 2003 Familiar Mathematical Relationships  Greater than  Not equal to  Less than or equal  Greater than or equal

5. SKUBIS © 2003 NEW Mathematical Relationship Proportional to

6. SKUBIS © 2003 Three Types of Proportions direct proportion indirect proportion (inverse) direct proportion to a square

7. SKUBIS © 2003 Now slowly, one at a time… Graphical Analysis of Motion

8. SKUBIS © 2003 The Direct Proportion “y is directly proportional to x”

9. SKUBIS © 2003 A Direct Proportion Example In straight line motion, “distance is directly proportional to time” Given more time, you can drive farther

10. SKUBIS © 2003 Changing a Proportion into an Equality Once again, consider…

11. SKUBIS © 2003 Changing a Proportion into an Equality 1. Replace with “=” 2. Multiply by a constant “k”

12. SKUBIS © 2003 Changing a Proportion into an Equality The constant “k” is an arbitrary letter… essentially, we could have used the symbol of our choice, “m” for example…

13. SKUBIS © 2003 Changing a Proportion into an Equality Look familiar? It should. The “m” indicates the slope of a straight line, which is exactly what a graph would look like if plotted.

14. SKUBIS © 2003 Direct Proportion’s Graph

15. SKUBIS © 2003 Recognizing a Direct Proportion - 1 When the variables in question are … On opposite sides of the equal sign and both in numerator or both in denominator

16. SKUBIS © 2003 Recognizing a Direct Proportion - 2 When the variables in question are … On the same side of the equal sign and one in numerator and one in denominator

17. SKUBIS © 2003 Take a Breather Get ready for the next proportion.

18. SKUBIS © 2003 The Indirect (inverse) Proportion “y is indirectly proportional to x”

19. SKUBIS © 2003 An Indirect Proportion Example In accelerated motion, Given less time, your acceleration rises

20. SKUBIS © 2003 Changing a Proportion into an Equality 1. Replace with “=” 2. Multiply by a constant “k”

21. SKUBIS © 2003 Changing a Proportion into an Equality For argument sake, let “k” =1 Look at how the values of “y” vary YX 11 0.52 0.333 0.254 0.205 0.1676 What do you think this plot will look like?

22. SKUBIS © 2003 Indirect Proportion’s Graph

23. SKUBIS © 2003 Indirect Proportion’s Graph hyperbola

24. SKUBIS © 2003 Recognizing an Indirect Proportion - 1 When the variables in question are … On opposite sides of the equal sign and one in numerator and the other is in denominator

25. SKUBIS © 2003 Recognizing an Indirect Proportion - 2 When the variables in question are … On the same side of the equal sign and both in numerator or both in denominator

26. SKUBIS © 2003 Take a Breather Get ready for the next proportion.

27. SKUBIS © 2003 “y is directly proportional to x-squared” The Direct Proportion to a Square

28. SKUBIS © 2003 In accelerated motion, As time increases, the distance traveled also increases The Direct Proportion to a Square Example

29. SKUBIS © 2003 Changing a Proportion into an Equality 1. Replace with “=” 2. Multiply by a constant “k”

30. SKUBIS © 2003 Changing a Proportion into an Equality For argument sake, let “k” =1 Look at how the values of “y” vary YX 11 42 93 164 255 366 What do you think this plot will look like?

31. SKUBIS © 2003 Direct Proportion to a Square Graph

32. SKUBIS © 2003 Direct Proportion to a Square Graph parabola

33. SKUBIS © 2003 Recognizing a Direct Proportion to a Square - 1 When the variables in question are … On opposite sides of the equal sign and both in numerator or both in denominator

34. SKUBIS © 2003 Recognizing a Direct Proportion to a Square - 2 When the variables in question are … On the same side of the equal sign and one in numerator and one in denominator

35. SKUBIS © 2003 Proportion Practice Identify any and all proportions from the following physics equations.

36. SKUBIS © 2003 Proportion Practice Identify any and all proportions from the following physics equations.

37. SKUBIS © 2003 Proportion Practice Identify any and all proportions from the following physics equations.

38. SKUBIS © 2003 Back to Smart Notebook Graphical Analysis of Motion Practice Qualitative Graphical Analysis