Unit 1 Notes

Linearizing a GraphIf 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.

Ex.t (s) Pos (m)

1 12 43 94 165 25

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

5

10

15

20

25

30

Time (s)

Posi

ton

(m)

The graph of y vs x is an upward opening parabola, so the graph will show y vs x^2.

Please note how the first column and the x-axis are labeled.

t^2 (s^2) Pos(m)1 14 49 9

16 1625 25

0 5 10 15 20 25 3005

1015202530

t^2 (s^2)

Pos

(m)

Before doing anything else, come up with the equation for the linearized graph.

Start by drawing a trend line and finding its slope.

mm=1(m/s^2)

0 5 10 15 20 25 3005

1015202530

t^2 (s^2)

Pos

(m)

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 + bPos = m t^2 + bUsing the point (25s^2, 25m),25 = 1 *25 + bb=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:

0 5 10 15 20 25 300

5

10

15

20

25

30

t^2 (s^2)

Pos

(m)

Written relationship: Position is proportional to the square of time.

Physical Meaning of Slope: As time squared increases by 1 s^2, position increases by 1m.

Math model:X=1(m/s^2) t^2

Meaning of Y-Intercept

When x is 0, y is b.

From the example, b=0.

When time^2 is 0, position is 0.