1. Position Vector. position of an object

2. Velocity Vector . change in position over time.

3. acceleration is change in velocity over time.

good.

I know the direction it is facing by using sin and cos thetha..

can i not use the the direction vector as my velocity?

You can, but why would you? Position is calculated from velocity, not the other way around.

How do i use the velocity vector to move in the direction in which i am facing?

The things is that the direction you're facing can be different from the direction you're traveling. Think cars on an icy road. Facing is useful, however, if you want to work with car-like physics - to accelerate, you'd apply a force in the direction the car is facing.

How do i get the acceleration of the player:

force = mass * acceleration;

acceleration = force/mass;

do i just set mass and force to be a random value?

You can use any units you want, but it might be easiest to keep track of real-world values: force in newtons and mass in kilograms.

Force is a vector, by the way. So, to implement some simple gravity in the z-direction, in pseudo-code:

Code:

acceleration = <0,0,m*g> / m; //a = f/m, gravity force = m*g, positive z is down
velocity += acceleration * dt; //dt = elapsed time since last update
position += velocity * dt;

Note that if you have multiple forces acting on an object, you'd just add them together and stick the sum into your a=f/m equation.

I'd recommend these articles as an intro to game physics.