Motion in two dimension #1

In summary: What do you get for the individual components of the velocity (vx and vy)?vx = 8.91 m/svy = 5.81 m/sIn summary, the particle moves at a speed of 8.91 m/s in the x direction and 5.81 m/s in the y direction.
  • #1
im4rheal
8
0

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?


Homework Equations


Basic Equations


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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  • #2


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.
 
  • #3


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?
 
  • #4


Ok, can I use the Vxf (velocity in the x direction, final) = Vxi + ax*t to find t?
 
  • #5


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 traveled Δx, which you DO know?
 
  • #6


Is it v^2xf = v^2xi + 2ax(xf-xi) ?
 
  • #7


im4rheal said:
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.
 
  • #8


im4rheal said:
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.
 
  • #9


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?
 
  • #10


im4rheal said:
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)
 
  • #11


Ok thanks
 
  • #12


cepheid said:
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?
 
  • #13


im4rheal said:
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".
 
  • #14


I got 8.91 m/s. Correct?
 
  • #15
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:

1. What is the difference between scalar and vector quantities in two-dimensional motion?

In two-dimensional motion, scalar quantities only have a magnitude (size) and no direction, while vector quantities have both magnitude and direction.

2. How do you calculate the displacement of an object in two-dimensional motion?

The displacement of an object in two-dimensional motion can be calculated using the Pythagorean theorem, where the displacement is the hypotenuse of a right triangle formed by the horizontal and vertical components of the displacement.

3. What is the equation for calculating the average velocity in two-dimensional motion?

The equation for average velocity in two-dimensional motion is v = (Δx/Δt, Δy/Δt), where Δx and Δy are the changes in position in the x and y directions, and Δt is the change in time.

4. How is acceleration calculated in two-dimensional motion?

In two-dimensional motion, acceleration is calculated by finding the change in velocity in both the x and y directions and dividing by the change in time, using the equation a = (Δvx/Δt, Δvy/Δt).

5. Can an object have constant velocity and changing acceleration in two-dimensional motion?

Yes, an object can have constant velocity and changing acceleration in two-dimensional motion. This can occur when the object is moving at a constant speed in one direction, but the direction of its velocity is changing, causing its acceleration to change.

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