Body trajectory and force direction

Hello Forum,

Let's consider a particle that is giving an initial speed in a certain direction. The particle is now moving in that initial direction at a constant speed.
If a later moment a force starts acting on the particle and the force direction is not along the original particle direction of motion, will that applied force eventually pull the particle in such a way that the particle travels along the force direction?

If I think of projectile motion with the object launched at a certain angle to the horizontal direction, the particle will trace an inverted parabolic path. The force of gravity is always pointing straight down and the particle direction (velocity vector direction) never ends up pointing exactly along the vertical direction....Would it if enough time was allowed to pass and the vertical distance was large enough?

Another situation: centripetal force. No matter what, if the force is perpendicular to the particle direction, the particle will change direction but will never end up pointing along the force direction....

what is the general concept?

thanks,
foggy37