Yes, the molecules of a gas are constantly in a random motion if the gas temperature is more than 0 degree kelvin. This random motion determines the average kinetic energy of the molecules which is equal to the temperature of the gas.
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No, they are in motion in a liquid as well. In a solid they vibrate in place.
"What are length constant and wedge constant in newton's laws of motion?"
No, the gas constant, or any constant, is constant meaning it doesn't change.
If constant motion means constant velocity then, total distance / total time = avg velocity => avg speed constant velocity => avg velocity = velocity
changing. only under specific requirements would the motion be constant.