Acceleration is (-2.0i + 4.0j), velocity is 12 m/s

AI Thread Summary
The discussion revolves around a particle's motion in the xy plane, characterized by an initial velocity of 12 m/s in the positive x direction and a constant acceleration of (-2.0i + 4.0j) m/s². To find the x coordinate when the y coordinate is 18 m, participants explore relevant equations of motion, including rf = ri + vit + 1/2at². The conversation highlights the need to integrate acceleration to derive velocity as a function of time and then use that to find the position. Participants express confusion about the calculations and seek clarity on applying calculus tools to solve the problem. The thread emphasizes the importance of correctly applying kinematic equations to determine the particle's position.
new^2^physics
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Homework Statement



At T=0 a particle leaves the origin with a velocity of 12 m/s in the positive x direction and moves in the xy plane with a constant acceleration of (-2.0i + 4.0j)m/s^2. At the instant the y coordinate of the particle is 18 m, what is the x coordinate of the particle.

Homework Equations



rf=ri + vit + 1/2at2
=(12m/s)(t) + 1/2 (-2.0i + 4.0j)t2

So stuck. Any direction or help would be greatly appreciated!
 
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so you know initial velocity to be 12.0i..
now you also know a = dv/dt
and v = dr/dt (r being position)..

Which mathematical (or calculus) tool can you use to get your answer now? and how?
 
Okay, so I am going to play with these equations and try to get closer...

a = dv/dt
(-2.0i + 4.0j)= 12i / dt

dt = 12i / -6.0i + 4.0j
dt = -6.0i - 4.0 j

v = dr/dt
12 i = xi - 18j / -6.0i - 4.0j
12i(-6.0i - 4.0 j) = xi - 18j

oh dear, now I am stuck again and I am not even sure I have done this part correctly.
 
new^2^physics said:
Okay, so I am going to play with these equations and try to get closer...

a = dv/dt
(-2.0i + 4.0j)= 12i / dt


that isn't correct...

a=dv/dt
(-2.0i+4.0j)dt=dv
integrating

-(2t)i + (4t)j = v-12

so you get v as a function of time... now proceed in a similar manner...
 
new^2^physics said:
At T=0 a particle leaves the origin with a velocity of 12 m/s in the positive x direction...

So, what are V_{ix}[/tex] and V_{iy}[/tex]?
 
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