Solving for Velocity and Acceleration Error: A Confusing Task

[h6872]

Hi everybody!

This might seem like a terribly easy question, but I can't seem to figure it out for the life of me. I've been given a set of values for time and velocity:

t (s) v (m/s)
0 0
3 7
7 16
12 33
18 48
23 53
27 67
34 86

And told that the errors at (delta)t = 0.2 s and (delta)v = 3.0 m/s are the same for all experimental points.

How would I go about determining the error for these values individually (as I'll have to graph the points)? The question asks for the acceleration and error, and the method I've been given seems to involve plotting each point with its associated error bars.

But couldn't I use the slope of my graph (if I plot these points without the error bars) to determine acceleration, and take the acceleration calculated from 3.0/0.2 as my expected value, and use the: (|your value-standard value|)/standard value equation?

And yet, I've been explicitly told not to consider this difference an error.

Please help! I'm completely confused!

 

[malawi_glenn]

Homework?

 

[sir-pinski]

Hello there! Solving for velocity and acceleration error can definitely be a confusing task, but I'm here to help. First, let's start with the concept of error. In this case, we are looking at the difference between the measured value and the true value. So, in your case, the error for each point would be the difference between the measured velocity and the expected velocity (calculated from the slope of your graph). You can then use the formula (|measured value - expected value|)/expected value to calculate the percentage error for each point.

Now, for the acceleration, you are correct in thinking that you can use the slope of your graph to determine the acceleration. However, it's important to also consider the errors for each point. This is where the error bars come in. By plotting the points with their associated error bars, you can see the range of possible values for each point. This allows for a more accurate calculation of the acceleration and its associated error.

So, to summarize, you can use the slope of your graph to determine the acceleration, but it's important to also consider the errors for each point and use them to calculate the overall error for the acceleration. I hope this helps clarify things for you and good luck with your calculations!