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Motion in two dimension #1

  • Thread starter im4rheal
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1. Homework Statement
At t=0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i - 4.0j)m/s^2. At the instant the x coordinate of the partice is 15 m, what is the speed of the particle?


2. Homework Equations
Basic Equations


3. The Attempt at a Solution
I'm not sure how to begin this problem, any help would be awesome. Keep in mind this is my first physics class so keep it as simple as possible. Thank you.
 

cepheid

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Re: Motion in two dimension

Welcome to PF im4rheal,

I'm sure you know the kinematics equations for constant acceleration. You can treat the x and y motions separately. So you just have to apply these equations for the motions in each direction. For the x direction:

- you know 'a'
- you know 'd' (or Δx)
- you know 'v0' (initial velocity)

You don't know t, or v, at the position in question, but all you need is two kinematics equations and you can solve for these two unknowns.
 

haruspex

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Re: Motion in two dimension

Amongst your 'basic equations', do you have one that tells you a relationship between a constant acceleration, an initial speed, a distance travelled, and a final speed? If so, can you write this out with known values in the x-direction?
 
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Re: Motion in two dimension

Ok, can I use the Vxf (velocity in the x direction, final) = Vxi + ax*t to find t?
 

cepheid

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Re: Motion in two dimension

That's one of the equations you need to use, but you don't know what vxf is, so you need another equation as well.

How about one incorporating the distance travelled Δx, which you DO know?
 
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Re: Motion in two dimension

Is it v^2xf = v^2xi + 2ax(xf-xi) ?
 

haruspex

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Re: Motion in two dimension

Is it v^2xf = v^2xi + 2ax(xf-xi) ?
Confusing notation, but that's basically it. (If you can't be bothered to use superscript and subscript, at least use '*' for multiply and maybe mixed case to represent subscripting, like Vx.)
You'll also need to figure out the time so as to get the velocity in the y direction.
 

cepheid

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Re: Motion in two dimension

Is it v^2xf = v^2xi + 2ax(xf-xi) ?
Well, yeah. I mean, you know all but one of the things in that equation, and it is the thing you are trying to solve for. So, of course this should work.
 
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Re: Motion in two dimension

Sorry I don't know how to do superscript and subscript. I should be able to find time from the first equation for solving for t right?
 

cepheid

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Re: Motion in two dimension

Sorry I don't know how to do superscript and subscript. I should be able to find time from the first equation for solving for t right?
Yup! You can get t from the equation in post #4, once you have vxf.

Try the sup and sub tags:

[noparse] vxf2 [/noparse]

to get this result:

vxf2

OR just use the buttons marked X2 and X2 that appear above the reply box, when you are in advanced reply mode (not quick reply)
 
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Re: Motion in two dimension

Ok thanks
 
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Re: Motion in two dimension

Well, yeah. I mean, you know all but one of the things in that equation, and it is the thing you are trying to solve for. So, of course this should work.
For the value of ax is it 2 m/s2?
 

cepheid

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Re: Motion in two dimension

For the value of ax is it 2 m/s2?
Yeah, this is given in the problem. The x-component of the vector is one with unit vector "i", and the y-component has unit vector "j".
 
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Re: Motion in two dimension

I got 8.91 m/s. Correct?
 

cepheid

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I get a different answer. Can you post your whole solution please? Otherwise we can't help you fix any errors that might be there...

What do you get for the individual components of the velocity (vx and vy)?
 
Last edited:

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