Basic Kinematics: Analyzing Distance v Time and Distance v t^2 Graphs

[dauerbach]

Just finished an experiment that seems totally screwed up. We let a roller decend an inclined plane of 7 and 9 degrees respecitvely and let it roll from 25 to 50 cm in increments of 5 cm. We then graphed distance v. time and distance v t^2. I thought the first should be a log scale, the second a straight line, but I couldn't get a good fit. What should these graphs tell me about the motion of the roller? How do I compute the acceleration due to gravity from the GRAPHS?

 

[jmb88korean]

if distance vs time gives you velocity, doing distance vs time gives you velocity, which vs. time gives you acceleration. slope of second graph is acceleration

 

[Paulie323]

I am not positive if this is what you were asking but, to find the acceleration vs time graph just derive the velocity vs time graph this will give you a linear graph of acceleration.

 

[zhermes]

I thought the first should be a log scale, the second a straight line

You're exactly right. The first should be exponential (what simple equation tells you this?), and the second linear.

but I couldn't get a good fit.

This could just be due to bad experimental setup (e.g. weird frictions, timing inaccuracies, etc).

What should these graphs tell me about the motion of the roller? How do I compute the acceleration due to gravity from the GRAPHS?

What should (hypothetically) the slopes of each graph be?

 

[rwisz]

First of all, it is important to note that the results of any experiment can sometimes be unexpected or appear to be "screwed up." This is a normal part of the scientific process and it is important to carefully analyze the data to understand what may have caused any discrepancies.

In terms of the graphs you have created, it is important to understand the relationship between distance, time, and acceleration. The distance v. time graph should show a linear relationship if the roller is moving with a constant speed. However, if the roller is accelerating, the graph will show a curved line. The distance v. t^2 graph should show a straight line if the acceleration is constant.

Based on the information provided, it seems that the roller may have been accelerating down the inclined plane. This would explain the lack of a good fit for the distance v. time graph and the curved line on the distance v. t^2 graph. To compute the acceleration due to gravity from these graphs, you can use the slope of the distance v. t^2 graph. The slope represents the acceleration, and since gravity is the only force acting on the roller, it should be equal to the acceleration due to gravity.

In order to get a more accurate result, it may be helpful to repeat the experiment multiple times and take an average of the results. Additionally, it may be useful to use more precise measurement tools and increase the range of distances measured to get a better understanding of the motion of the roller.

Overall, these graphs can tell you a lot about the motion of the roller and can help you calculate the acceleration due to gravity. However, it is important to carefully analyze the data and consider any potential sources of error to ensure accurate results.