Comparing Accelerations from Velocity Functions

[Loppyfoot]

Homework Statement

Compare the acceleration that you found by your velocity function, to the acceleration of the function of the object that I found by taking the derivative.

Homework Equations

v(t) = 0.9t – 2
Then through an xy scatter, I got this equation for the velocity:
v(t) = 0.6 - 4t + 5t² -2t³ + 0.2t⁴
Then I found the acceleration function by taking this derivative.
How do I compare the acceleration of the line regression: 0.9m/s² to the function I found by taking the derivative?

 

[jbsteele]

The AnswerTo compare the acceleration of the linear regression (0.9 m/s2) to the acceleration function found by taking the derivative, you can evaluate the acceleration function at various values of t and compare the results. For example, if t = 0, then the acceleration of the linear regression is 0.9 m/s2, while the acceleration of the function found by taking the derivative is 0.6 m/s2. Similarly, if t = 1, then the acceleration of the linear regression is still 0.9 m/s2, while the acceleration of the function found by taking the derivative is -3.4 m/s2. As you can see, the acceleration of the two functions differ significantly at different points.

 

[tomcue]

I would like to commend you on your efforts in finding the acceleration function through both methods. It is always important to compare and validate our results through different approaches in order to ensure accuracy and reliability.

In this case, we have two different methods for finding the acceleration function: one through a linear regression of the velocity data and the other through taking the derivative of a polynomial function. While both methods may lead to the same result, it is important to note that there may be slight variations due to the nature of the data and the calculations involved.

To compare the two accelerations, we can plot them on a graph and observe the similarities and differences. We can also calculate the numerical values and compare them to see if they are within a reasonable range of each other. Additionally, we can also perform statistical analyses to determine the correlation and significance between the two acceleration functions.

Overall, it is important to carefully analyze and interpret the results from both methods in order to confidently determine the acceleration of the object. Thank you for bringing this comparison to my attention, as it highlights the importance of critically evaluating our methods and results in scientific research.