Physics Olympiad Vector Acceleration

AI Thread Summary
The discussion revolves around a physics problem involving a particle of mass 2.00 kg subjected to a force that results in a non-constant acceleration. The initial velocity of the particle is given, and the task is to determine the time it takes for the particle to return to the origin and the maximum distance from the origin. The user initially attempts to apply the equations of motion but encounters issues due to the non-constant nature of the acceleration. Suggestions are made to consider calculus for solving the problem, particularly using derivatives to analyze the motion. The conversation highlights the complexity of the problem and the need for a deeper understanding of dynamics and acceleration.
bazookajason
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Homework Statement


A particle of mass 2.00 kg moves under a force given by
F~ = −(8.00 N/m)(xˆi + yˆj)
whereˆi and ˆj are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity~v = (3.00 m/s)ˆi + (4.00 m/s)ˆj.

a. After how much time will the particle first return to the origin?
b. What is the maximum distance between the particle and the origin?



Homework Equations


f=ma
x=vt+1/2at^2


The Attempt at a Solution


Using f=ma, i find the acceleration to be a=-4x i + -4y j
Using x=vt+1/2at^2, if i set x as 0
So i get 0=3t+1/2(-4x)t^2 and 0=4t+1/2(-4y)t^2
I solve those 2 equtaions to get 3y=4x
but i don't know where to continue
 
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bazookajason said:

Homework Statement


A particle of mass 2.00 kg moves under a force given by
F~ = −(8.00 N/m)(xˆi + yˆj)
whereˆi and ˆj are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity~v = (3.00 m/s)ˆi + (4.00 m/s)ˆj.

a. After how much time will the particle first return to the origin?
b. What is the maximum distance between the particle and the origin?

Homework Equations


f=ma
x=vt+1/2at^2

The Attempt at a Solution


Using f=ma, i find the acceleration to be a=-4x i + -4y j
Using x=vt+1/2at^2, if i set x as 0
So i get 0=3t+1/2(-4x)t^2 and 0=4t+1/2(-4y)t^2
I solve those 2 equations to get 3y=4x
but i don't know where to continue
The equation
x=vt+(1/2)at2
has 2 big problems.
1. It's only true for uniform (constant) acceleration. The acceleration here is not constant.

2. Even if the acceleration were constant you should only have included x components.​
 
hm do i use calculus?
a= derivative of x
 
anyone?
 
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