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 one year 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 xdot?
So for example, if they give x=2t and that's in terms of velocity, it's xdot? And then the derivative of that for acceleration would be xdouble dot?
 one year 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 xdot? So for example, if they give x=2t and that's in terms of velocity, it's xdot? And then the derivative of that for acceleration would be xdouble dot?

This Question is Closed

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1Furthermore, say you have a velocity position function y=x^2. Would the chain rule for that be y = 2x*(xdot)? If you're confused by when I say xdot, I'm talking about this: http://web.mst.edu/~reflori/be150/Dyn%20Lecture%20Videos/Particle%20Kinem%20

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1uhh, it's currently being updated. I'll read up on xdot and see what I think is the answer.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1Oh, it is? Interesting. I'm studying dynamics this quarter and the notation is very new and confusing to me.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1What do you mean by x=2t is given in terms of velocity?

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1It's a parametric equation

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1okay, is that the full details?

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1if you have a y parameter and you are looking for the velocity it's defined differently.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1So you'll have an xfunction in terms of t, and then a yfunction in terms of x. The xyfunction is position.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1Just a sec, I can post the few pages out of Hibbeler's book. Hold on.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1Yes. 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.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1Example 12.10 gives a lot of insight, but I'm still not completely clear on everything.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1ohh  what are you having trouble with?

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1I was wondering if I was given a parametric equation in terms of x and t that is velocity, if that would be considered xdot.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1if there was just x and t. If there were more variables, such as in this example, it is not just xdot.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1What 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 xdot would be the velocity.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1but the example has y, which is really afunction of t, although it is given in terms of x. So you need to use the twodimensional definition of velocity.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1what I got stuck on is after you do the chain rule for the yfunction in terms of x... and then you're plugging in your x, xdot, and xdoubledot if you were to accidentally plug in xdot for x. Sorry if it sounds like I'm speaking in riddles!

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1I think I'll go in and bug my instructor tomorrow morning :)

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1instead of using xdot try to use \(V_x\) if you are allowed to,

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1xdot is a simple way of saying the change of x with relation to t.

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.1just 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.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1I 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.

brinethery
 one year ago
Best ResponseYou've already chosen the best response.1Let me know if you have any new insight :)
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