# Mechanics with vectors question

• simpleas123
In summary, the conversation discusses a question involving a particle and its motion. The first part involves writing equations for the force and motion of the particle. The second part involves finding initial conditions. The final part discusses the trajectory equation and how to find a relationship between x and y.

#### 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 :)

Last edited by a moderator:
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.