Mechanics with vectors question

[simpleas123]

Alright all I've been attempting this question and I've become stuck.

This is the question.

Homework Statement

http://img707.imageshack.us/img707/2575/63353658.jpg [Broken]

Homework Equations

In the working out.

The Attempt at a Solution

So for the first part i wrote F=Mx^.. (X double dot).
I also stated that if there was no force acting on the particle then the particle would stay at a constant speed V if we ignored instances such as the particle being on a slope.

For the second part i wrote (Im using X to denote x hat (x^^), same applied with y.)

F_x X + F_y Y = m x^.. X + m y^.. Y

=> x^.. = 2 , y^.. = 3x^2

Now for the third part when writing down the inital conditions this is where i become confused. Shall i write it in plain english such as;

At time equal to 0, this displacement of the particle x^.. will be 0.

Im not too sure how to answer that part, or the last part.

Any help is greatly appricated cheers people :)

 

[aim1732]

For the trajectory eqn. you can integrate the two eqn. you got in the previous part twice w.r.t time . Then eliminate the t from the two eqn. to obtain the relationship b/w x and y.