Quasi-creature plants

What is a quasi-creature plant?

I define a quasi-creature plant as an organism that lives only through photosynthesis that moves with a speed in the same order of magnitude of that of an animal.

Here on Earth, almost nothing

On Earth almost all plants move very slowly, orders of magnitude more slowly than animals. It is because the low energy provided by the Sun does not allow waste of movement.

What kind of potential environments would be good fits?

In what kind of situations, if any, would a plant moving with a speed in the same order of magnitude of that of an animal be possible? Maybe orbiting around a blue star, more light would get to the surface, or a binary system with the right timing could make the planet almost night-less, doubling the energy available for photosynthesis.

Is it more probable to be in air, water or ground?

Ground

Even something like a plant with a huge green surface over itself that stays still most of the time, but when there are no predators (read: herbivores) it moves using tiny legs hidden underneath to get more sun?

Water

Maybe as water is where the life started this would easiest with a creature spending most time in the dark fondal but raising to near the surface where few predators are nearby.

Air

Or a flying(?!) plant with a huge membrane that gives it great aerodynamics and at the same time takes much sun, it would swing the wings very slowly not to end up its energy and rest atop trees when there is not enough sun?