SKUBIS © 2003 Graphical Analysis of Motion

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

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

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

SKUBIS © 2003 NEW Mathematical Relationship Proportional to

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

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

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

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

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

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

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…

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.

SKUBIS © 2003 Direct Proportion’s Graph

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

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

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

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

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

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

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

SKUBIS © 2003 Indirect Proportion’s Graph

SKUBIS © 2003 Indirect Proportion’s Graph hyperbola

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

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

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

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

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

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

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

SKUBIS © 2003 Direct Proportion to a Square Graph

SKUBIS © 2003 Direct Proportion to a Square Graph parabola

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

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

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

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

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

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