Particles are displaced perpendicular to motion (up and down) in which kind of
wave?

Transverse
Or
Longitudinal

Transverse wave= Oscillations where particles are displaced perpendicular to the wave direction

A blackboard, also called a chalkboard, is a surface on which markings made with chalk are visible. Whiteboards are used because some people are allergic to the dust the chalk used to write on chalkboards generate, and because the dust is hard to clean up when spilled.