Deriving an equation for the velocity of a particle

[LonelyElectron]

Homework Statement

Derive an equation for the velocity vx(t), vy(t) of the particle. - my teacher writes this oddly, that means the velocity in the x direction at any point in time, and the velocity in the y direction at any point in time.
Calculate the initial velocity of the particle.
Calculate the velocity of the particle at t=2 and discuss why it is/isnt the same as the average velocity.

Homework Equations

I have to derive one??

The Attempt at a Solution

From previous questions I have the following:
-displacement in the x direction = 9 units
-displacement in the y direction = -6.75 units
-time in the x and y direction = 3 seconds
-average velocity in the x direction = 3 units a second
-average velocity in the y direction = -2.25 units a second
-through first and second differences we know that velocity is not constant, but acceleration is constant for both axis
-acceleration in the x direction = 2 units a second squared
-acceleration in the y direction = -1.5 units a second squared
-because acceleration is constant average acceleration = instantaneous acceleration

If velocity were linear I would use y=mx+b, but as it stands I have no idea where to go... Any help is really appreciated...I have included a picture of my sheet in case I was not clear.

Thanks!

 

[Gene Naden]

I am having a little trouble reading the image you attached. Also, where you write "displacement in the x direction = 9", I do not know whether this is at time t2 or time t1. Likewise for "displacement in the y direction = -6.75", etc.
If you can clean it up a little, I will try to help you.

By the way, the velocity is in fact linear. That is, if you plot velocity versus time, it will be a straight line.

Good luck!