Finding Acceleration from a v^2 vs. t Graph

[ethinh]

Homework Statement

when graphing a velocity squared vs. time graph how do I find the acceleration. I realize the slope gives me units of acceleration but this is not correct because the theoretical acceleration is no where near this and I didnt botch this lab up.

Theoretical
a = gsin(3.03) +/- 0.085 m/s^2

when i graph my data from the photogate the linear trend line gives me a slope of 1.0481 which is the acceleration in this case but like I said that is far beyond the theoretical.

also i did this experiment by using a stopwatch and I calculated an acceleration using the equation
a=2s/t^2 and got an acceleration of 0.58 +/- 0.10 m/s^2

So again how do I calculate the correct acceleration using a v^2 vs. x graph?

 

[Simon Bridge]

Homework Statement

when graphing a velocity squared vs. time graph how do I find the acceleration. I realize the slope gives me units of acceleration but this is not correct because the theoretical acceleration is no where near this and I didnt botch this lab up.

The slope of the velocity-time graph is the acceleration.

But you wrote: "velocity-squared vs time" ... the slope of that graph will not give you the acceleration.
If you means "displacement-squared vs time" then that is also wrong ... as you can see by rearranging your own equations from later: a=2s/t^2 means s=(a/2)t^2 ... i.e. a plot of s vs t^2 gives a slope of a/2.

But it may be a typo - in which case there is probably something else going on that you have not taken into account with the theory.

 

[ethinh]

Thanks Simon but I figured out that I had to use a kinematics equation V^2=2a(xf-xi) to find acceleration and it matched the theoretical value pretty well!

 

[Simon Bridge]

OK. So what did you plot?

 

[Nickie]

I understand your frustration with obtaining different values for acceleration from different methods of measurement. It is important to note that there can be variability in experimental data due to various factors such as human error, equipment limitations, and external influences. Therefore, it is always important to compare your results to theoretical values and take into account any potential sources of error.

In terms of finding acceleration from a v^2 vs. t graph, the slope of the graph does indeed give the units of acceleration. However, it is not always accurate due to the limitations of the equipment and experimental setup. It is also important to check for any outliers or discrepancies in your data.

One approach to obtaining a more accurate value for acceleration is to use multiple methods of measurement and compare the results. In your case, you have used both the photogate method and the stopwatch method. It is recommended to take an average of these values to minimize any potential errors.

Additionally, it is important to consider the accuracy of your theoretical value for acceleration. Is it based on a simplified or idealized model? Are there any external factors that could affect the theoretical value? These are important questions to consider when comparing your experimental results to the theoretical value.

In conclusion, finding the correct acceleration from a v^2 vs. t graph requires careful consideration of experimental methods, potential sources of error, and comparison with theoretical values. It is important to be aware of the limitations of your equipment and experimental setup, and to use multiple methods to obtain a more accurate result.