Practice Problems: Graphing
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1. A car accelerates from rest along a straight line. Its velocity (v) is measured at different times (t):
t (s): 0, 2, 4, 6, 8
v (m/s): 0, 8, 16, 24, 32

Graph this data as velocity vs. time and determine the type of mathematical relationship that exists between the variables. Also, find the equation that shows the relationship.

2. A student investigates the relationship between the pressure (P) and volume (V) of a fixed amount of gas at constant temperature:
V (Liters): 1.0, 2.0, 3.0, 4.0, 5.0
P (atmospheres): 5.0, 2.5, 1.67, 1.25, 1.0 

Graph this data as pressure vs. volume and determine the type of mathematical relationship that exists between the variables. Also, find the equation that shows the relationship then use that equation to predict the pressure when the volume is 3.5 Liters.

3. A student measures the period (T) of a pendulum, the time it takes for one complete swing, for different lengths (L). The data is as follows:
L (m): 0.2, 0.4, 0.6, 0.8, 1.0
T (s): 0.89, 1.26, 1.55, 1.79, 2.00
Create 2 graphs: The first is Period vs. Length and the second is Period Squared vs. Length. Identify the mathematical relationships shown in each one. What advantage does the second one have over the first? Find the equation for the line of best fit in the second graph. Use that equation to find the period when the length is 1.35 m.

4. Use the graphing simulation below to find the best fit linear equation for the following unitless data:
x-data: 0, 0.8, 2.1, 3.0, 4.0
y-data: 6.8. 5.0, 3.3, 2.7, 0
Use the equation to find the y-value when the x-value is 2.6
Click both the "curve" and "value" boxes to get the best fit line and to place the data point (the orange dots) at the correct positions. 

5.Use the graphing simulation below to find the best fit quadratic equation for the following unitless data:
x-data: 0, 2.4, 4.8, 6.8, 8.7
y-data: -0.1. 0.5, 1.2, 1.8, 3.7
Use the equation to find the y-value when the x-value is 5.2
Click both the "curve" and "value" boxes to get the best fit line and to place the data point (the orange dots) at the correct positions.
 

Textbook Assignment:

1. Answer questions 15 in the Concept Items section of the Chapter Review for Chapter 1.