motion - Move a 2D point to a target (first accelerate towards the target, then decelerate)

I have a point entity that I would like to move to a target point (in 2D).

I think I would like it to accelerate away from its current position (the point could already have a velocity), to some maximum velocity, and decelerate as it approaches the target, eventually coming to a stop on the target.

I think both the acceleration and deceleration should have constant magnitudes, but given that the entity can have a velocity, which may not be in the same direction as the target, the direction of the acceleration/deceleration could be different every frame.

I am not coding in any particular language or framework yet, and just want to know if this is easy/possible. Am I describing something that is quite common (like a targeted missile that stops at the target/an AI controlled space ship in a game)? If it is hard, is there another way I can achieve the same kind of motion?