Introductory Physics I - PHYS 200 -Lab 1- Graphical Analysis COMPLETE UPDATE NEW VERSION 2026 Athaba

Introductory Physics I - PHYS 200 | Lab 1Graphical Analysis COMPLETE UPDATE NEW VERSION 2026 Athabasca University

Lab 1: Graphical Analysis Physics 200, Athabasca University

Introduction Scientific studies and experiments aim to explore the relationships between physical quantities, which are categorized as independent and dependent variables. Independent variables remain unaffected by other factors in the study, while dependent variables vary based on changes in the independent variable(s). Dependent variables are also the focus of measurement or testing within an experiment.

Once these variables are identified and the dependent variable is measured, the data can be organized into tables and graphs to discern patterns and observe the effects of the independent variable on the dependent variable. Typically, the independent variable is represented on the x- axis, while the dependent variable is placed on the y-axis.

When plotted on a graph, the data points often exhibit a linear pattern, which can be quantified using the linear function: y = mx + b. Here, 'm' represents the slope, indicating the rate of change in 'y' for every change in 'x' (rise/run = Δy/Δx). The y-intercept of the linear equation, denoted by 'b', signifies the value of 'y' when 'x' is 0.

Procedure During a trip a friend and I took from Calgary to Edmonton I decided to keep myself busy by keeping a record of the distance travelled versus the time. While waiting for the last traffic light to turn green on the outskirts of Calgary, I reset the odometer to zero. When the light turned green, I started timing the trip with a stopwatch. Every ten minutes I recorded the odometer reading. Since the odometer gave the distance within 100m, I estimated the uncertainty to b +/- 0.1km, and I estimated a 12 second timing (+/- 0.2min) error even though I did my best to take the readings at 10 minute intervals.

Analysis and Discussion To better visualize the relationship between travel distance and time, Table 1 was created by converting elapsed time from minutes to hours, and then graphed in Figure 1. The graph reveals a linear correlation between the distance traveled in kilometers and the time elapsed in hours. Despite the absence of error bars, as they would have been too small to discern, the distance uncertainty of 0.1 km and time uncertainty of 0.003 hours would have been scarcely visible due to the substantial increments in the datasets (15 km and 0.16 hours).

Consequently, these uncertainties will arguably not affect the overall data.

By fitting a line to the data points, the approximate slope of the line was determined.

In this context, the slope of the best-fit line represents the average speed of the car throughout the journey.

Table 1: Distance travelled by the car versus time. To convert from minutes to hours, the time in minutes was multiplied by (1/60).

Time in Minutes tm±0.2(min)𝑡𝑚±0.2(min)

Time in Hours th±(h)𝑡ℎ±(h)

Distance d±0.1(km)𝑑±0.1(km)

0

0

0

10.0

0.167

17.5

20.0

0.333

34.5

30.0

0.500

52.5

40.0

0.667

76.1

50.0

0.833

87.0

60.0

1.00

105.0

70.0

1.17

122.3

80.0

1.33

144.0

90.0

1.50

152.3

100.0

1.67

177.0

110.0

1.83

191.1

120.0

2.00

209.0

130.0

2.17

227.4

140.0

2.33

241.0

150.0

2.50

263.7

160.0 170.0

2.67

285.2 292.1

2.83