## brinethery 2 years ago Quick question about derivatives involving Newton's dot notation and the chain rule: I was just wondering if, say you have a velocity function in terms of t, would that be considered x-dot? So for example, if they give x=2t and that's in terms of velocity, it's x-dot? And then the derivative of that for acceleration would be x-double dot?

1. brinethery

Furthermore, say you have a velocity position function y=x^2. Would the chain rule for that be y = 2x*(x-dot)? If you're confused by when I say x-dot, I'm talking about this: http://web.mst.edu/~reflori/be150/Dyn%20Lecture%20Videos/Particle%20Kinem%20

2. inkyvoyd

uhh, it's currently being updated. I'll read up on x-dot and see what I think is the answer.

3. brinethery

Oh, it is? Interesting. I'm studying dynamics this quarter and the notation is very new and confusing to me.

4. inkyvoyd

What do you mean by x=2t is given in terms of velocity?

5. brinethery

It's a parametric equation

6. inkyvoyd

okay, is that the full details?

7. inkyvoyd

if you have a y parameter and you are looking for the velocity it's defined differently.

8. brinethery

So you'll have an x-function in terms of t, and then a y-function in terms of x. The xy-function is position.

9. brinethery

Just a sec, I can post the few pages out of Hibbeler's book. Hold on.

10. inkyvoyd

Yes. Then, the velocity is actually defined to be sqrt ((x dot)^2+(y dot)^2). Although I probalby have less qualification than you to say this.

11. brinethery

12. brinethery

Example 12.10 gives a lot of insight, but I'm still not completely clear on everything.

13. brinethery

12.9 I mean

14. inkyvoyd

ohh - what are you having trouble with?

15. brinethery

I was wondering if I was given a parametric equation in terms of x and t that is velocity, if that would be considered x-dot.

16. inkyvoyd

if there was just x and t. If there were more variables, such as in this example, it is not just x-dot.

17. inkyvoyd

What is important to know is that in this example y is given in terms of x, but in reality we see y as a function of t. In a way, it's a composite function. If you are talking about just moving on say a number line, you would only have one direction to move in, and x-dot would be the velocity.

18. inkyvoyd

but the example has y, which is really afunction of t, although it is given in terms of x. So you need to use the two-dimensional definition of velocity.

19. brinethery

what I got stuck on is after you do the chain rule for the y-function in terms of x... and then you're plugging in your x, x-dot, and x-double-dot if you were to accidentally plug in x-dot for x. Sorry if it sounds like I'm speaking in riddles!

20. brinethery

I think I'll go in and bug my instructor tomorrow morning :-)

21. inkyvoyd

instead of using x-dot try to use \(V_x\) if you are allowed to,

22. inkyvoyd

x-dot is a simple way of saying the change of x with relation to t.

23. inkyvoyd

just have to be clear on what the variables are and what they mean. Y is the vertical *position* of the point, and X is the horizontal *position* of the point. t is time. We are interested in measuring the change of both x and y with respect to t in a way such that it makes sense.

24. brinethery

Exactly

25. brinethery

I thank you for your help and I'll have something to think about on this now. But I've gotta go make dinner and work on the physics that's been piling up. I'll be back later to check this thread. Thank you again.

26. inkyvoyd

Alright. Good luck!

27. brinethery

Let me know if you have any new insight :-)