Physics Simulation Forum

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