How would I calculate how much infrared light it would take to move an 80kg object (a person) say 1 meter per second...

energy to push object = mass * acceleration * distance

wavelength of infrared light ~ 700nm

energy of one photon = hc / wavelength

energy to push object / energy of one photon = number of photons

number of photons = mass * acceleration * distance * plank's constant * speed of light / wavelength

I have the answer to your question.

Cyclops possesses the mutant ability to project a beam of heatless ruby-colored concussive force from his eyes, which act as inter-dimensional apertures between this universe and another. Cyclops doesn't fire lasers, so calculating the potential kinetic energy found in the photons in infrared light to move a person would be pointless since Cyclop's beam isn't comprised of electromagnetic radiation.

how is it visible and red?

Sorry I fucked this up

energy to push object = energy of n photons = nhc / w = mad

n = wmad/hc

where n = number of photons, w = wavelength, m = mass, a = acceleration, d = distance, c = speed of light, h = plank's constant

so if the acceleration is 1 m/s2 and the distance is 1 meter, it would just be mass * acceleration, right?

Because it looks cool.

I think any particle, even if its made up magical particles, that have enough force to knock over people and literally carve tunnels through the earth, would definitely ingnite things and vaporise things.

Makes sense, at the speed his beam is travelling it would probably burn things due to friction with the air before impact. But the beam is not hot in nature as it's not comprised of electromagnetic radiation.

I think the kinetic energy of the particles hitting an object would release a lot of energy too.

And thanks for the tips guys, I think i've found was I was looking for.