# Motion in two dimension #1

#### im4rheal

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.

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#### cepheid

Staff Emeritus
Gold Member
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

Homework Helper
Gold Member
2018 Award
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?

#### im4rheal

Re: Motion in two dimension

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

#### cepheid

Staff Emeritus
Gold Member
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?

#### im4rheal

Re: Motion in two dimension

Is it v^2xf = v^2xi + 2ax(xf-xi) ?

#### haruspex

Homework Helper
Gold Member
2018 Award
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

Staff Emeritus
Gold Member
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.

#### im4rheal

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

Staff Emeritus
Gold Member
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)

#### im4rheal

Re: Motion in two dimension

Ok thanks

#### im4rheal

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

Staff Emeritus
Gold Member
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".

#### im4rheal

Re: Motion in two dimension

I got 8.91 m/s. Correct?

Staff Emeritus