Question on Calculus and Vectors

[EternalWrath]

Technically, I have a question for my physics class, but the problem relies more on calculus than anything else. I am given an acceleration in component form, and need to find equations for the velocity and position of the particle. What I forget is whether I integrate the components of the vector, or find the magnitude first and then integrate that.

Here's the actual problem for anyone interested: "Fx(t) = k1 + k2y and Fy(t) = k3t" The numbers are all subscripts, and the mass is just m.

I ask this here because, in my experience, people who frequent this forum are awesome at math. ^_^

[foilman8805]

Re: Question on Calculus and Vectors

To get from acceleration to velocity you have to integrate, and the same goes for velocity to displacement.

You want to integrate the whole acceleration vector (both directions), because that will result in the full velocity vector. Integrating the magnitude leaves out variables and such. Also, when you integrate, don't forget to add your constant of integration.

I'm not going to do the actual problem - just explain the guidelines. You are perfectly capable of doing it yourself.

[sayuncle990]

Re: Question on Calculus and Vectors

Ugh, if this wasn't calculus based I'd love to help you. The problem is my physics class didn't do any calculus. That being said, I don't know how this works.

I might be able to help however. From my physics I know that using cmoponents for acceleration is a pain. What we learned to do, and I don't know if you learned this yet, is to simply rotate your free-body diagram if you do that. That would make the acceleration along one of the axis, greatly reducing the complexity of the problem.

Good luck.

Edit: Oh, I was wondering if you do integrals in calculus based physics. That would make sense for velocity.

[EternalWrath]

Re: Question on Calculus and Vectors

Yeah, I integrated both the horizontal component and the vertical component, and got the components of velocity and displacement in terms of time. I can't verify that I got the right answer, but finding the magnitude seems far too troublesome to bother dealing with. Yes, I'm just lazy.