1. Graphical Analysis When we take data as scientist we need an efficient method for picking out trends, and noticing relationships (correlations) between the different parameters we are studying Graphs also help us predict the behavior of a physical system Being able to understand and interpret graphs is very important Extract abstract ideas about what you’re looking at

2. Graphical Analysis what type of things can we conclude from this graph? Which car went the fastest during any 1 second point of the race? Which car blew its engine? How far did the Ford travel between the 3rd second and the 5th second? What quantity does the slope of the line represent?

3. Graphical Analysis What makes a proper Graph? –A coordinate system Origin, defined and labeled Data Points, instructions on how they are defined Axes, defined, labeled, which way is increasing, units used 0 Displacement (m) Time (s) P (t 1, d 1 ) Q (t 2, d 2 ) t1t1 t2t2 d1d1 d2d2 origin data points axis arrow denotes the direction that is increasing values axis labels must have units on them

4. Independent Variable: Experimenter Controls (temperature, weight, time) Dependent Variable: Measurement (effect that changing the ind. variable had) Interval (x-axis) Dx = x 2 - x 1 Interval (y-axis) Dy = y 2 - y 1 0 Dependent Variable Independent Variable P (x 1, y 1 ) Q (x 2, y 2 ) x1x1 x2x2 y1y1 y2y2 yy Graphical Analysis

5. NO Relationship – Scatter Graph Y Does NOT Depend Upon X 0 X Y

6. Proportional Relationship As X increases, Y increasesY ~ X As X decreases, Y decreases 0 X Y

7. Inversely Proportional Relationship As X increases, Y decreasesY ~ 1/X As X decreases, Y increases 0 X Y

8. Nonlinear (Quadratic or exponential) 0 X Y As X increases Y increases much faster Y increases to a higher power (example area)

9. Length (m)Area (m 2 ) 11 24 39 416 525 636 749 864 981 10100

10. Time interval  t = t 2 - t 1 Distance (y-axis)  d = d 2 - d 1 m = Slope of the line 0 Distance (m) Time (s) P (t 1, d 1 ) Q (t 2, d 2 ) t1t1 t2t2 d1d1 d2d2 dd Distance = (Speed)  (Time) y = (m) (x) + b

11. Density  0 Volume (cm 3 ) Mass (grams) Water  water = 1.0 gr/cm 3 Ice Lead If something is going to float in water it’s density must be less than the density of water (1.0 gr/cm 3 ).

12. 0 Volume (cm 3 ) Mass (grams) Water Ice Lead Density  What if I were to ask you some questions about this graph. A 10 cm 3 volume of which substance would weigh the least? How would you go about answering this question? First you should ask yourself? What am I looking for? the substance with the lowest density will weigh the least!