Accurate and timely velocity-based movement

I am making a 2D-platformer and I'm wondering how one would handle movement that has to be both spatially accurate and on time without resorting to directly manipulating an object's position.

For example: A platform should move 5 units to the right over a time frame of 2 seconds. Ideally, its movement on the x-axis should describe a quarter of a sine-wave (0 to π/2) but any other type of movement that is not completely linear and does not start and stop abruptly would probably also suffice.

If somebody could help me out with this or point me to resources that could be useful for solving this, I would be very thankful.