Unit 1 Notes Linearizing a Graph If a

Unit 1 Notes

Linearizing a Graph If a graph from a lab does not show a linear relationship, you will have to make a modification to the data to linearize the graph. Pos (m) 1 1 2 4 3 9 4 16 5 25 Positon (m) Ex. t (s) 30 25 20 15 10 5 0 0 1 2 3 Time (s) 4 5 6

t^2 (s^2) Pos(m) 1 1 4 4 9 9 16 16 25 25 Pos (m) The graph of y vs x is an upward opening parabola, so the graph will show y vs x^2. 30 25 20 15 10 5 0 0 10 t^2 (s^2) 20 30 Please note how the first column and the x-axis are labeled.

Pos (m) • 30 25 20 15 10 5 0 0 10 t^2 (s^2) 20 30

Next, find the y-intercept. Start with the general form y=mx+b. In this case, y is Pos, x is t^2, and m is 1 m/s^2. Choose one point on the line and use its x- and y -values with the slope you already found. Y = mx + b Pos = m t^2 + b Using the point (25 s^2, 25 m), 25 = 1 *25 + b b=0

Now we have everything we need to finish the graph. Math Model: (the equation for your line) Pos = 1(m/s^2) t^2 Written Relationship: Position is proportional to the square of time. (found on the handout that goes on the inside of the front cover of your lab notebook) ***The written relationship does not change just because the graph has been linearized. ***

Physical meaning of slope: The general form is: As x increases by 1 (x-unit), y increases by m (y-units). In this case, As time squared increases by 1 second squared, position increases by 1 meter.

Write the written relationship, physical meaning of slope, and math model on the linearized graph: 30 Written relationship: Position is proportional to the square of time. Pos (m) 25 Physical Meaning of Slope: As time squared increases by 1 s^2, position increases by 1 m. 20 15 Math model: X=1(m/s^2) t^2 10 5 0 0 5 10 15 t^2 (s^2) 20 25 30

Meaning of Y-Intercept When x is 0, y is b. From the example, b=0. When time^2 is 0, position is 0.