Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

It's a parametric equation

Answer 6

okay, is that the full details?

Answer 7

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

Answer 8

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.

Answer 9

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

Answer 10

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.

Answer 11

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

Answer 12

12.9 I mean

Answer 13

ohh - what are you having trouble with?

Answer 14

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.

Answer 15

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

Answer 16

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.

Answer 17

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.

Answer 18

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!

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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.

Answer 23

Exactly

Answer 24

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.

Answer 25

Alright. Good luck!

Answer 26

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