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brinethery
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?
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
uhh, it's currently being updated. I'll read up on x-dot and see what I think is the answer.
Oh, it is? Interesting. I'm studying dynamics this quarter and the notation is very new and confusing to me.
What do you mean by x=2t is given in terms of velocity?
It's a parametric equation
okay, is that the full details?
if you have a y parameter and you are looking for the velocity it's defined differently.
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.
Just a sec, I can post the few pages out of Hibbeler's book. Hold on.
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.
Example 12.10 gives a lot of insight, but I'm still not completely clear on everything.
ohh - what are you having trouble with?
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.
if there was just x and t. If there were more variables, such as in this example, it is not just x-dot.
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.
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.
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!
I think I'll go in and bug my instructor tomorrow morning :-)
instead of using x-dot try to use \(V_x\) if you are allowed to,
x-dot is a simple way of saying the change of x with relation to t.
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.
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.
Let me know if you have any new insight :-)