I'm really new with physics. Maybe someone would be able to help me to solve the next problem:

I need to calculate position of an agent on the plane(2D) in next time step where time step is large(20+ seconds)

What I know about agent's motion:

-Initial Position

-Direction(normalised vector)

-Velocity(linear function from time ) - object always moves along it's direction

-Angular Velocity(linear function from time)

Optional:

-External force direction

-External force (linear function from time)

Running discreet simulation with t->0 is not a option...

I understand that it should not be difficult, just correct application of calculus probably, but I'm stuck