Physics Olympiad Vector Acceleration

[bazookajason]

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

 

[SammyS]

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.​

 

[bazookajason]

hm do i use calculus?
a= derivative of x

 

[bazookajason]

anyone?