[Yahya A.Sharif (OP)]

These are the three types of infinite motion in the universe of an object where this object travels infinite distance in infinite time.

1) An object moves in straight line this object will travel infinite distance in infinite time if we suppose that the object will not find some obstacle and the universe is infinite.

2) An object moves endlessly in a circle,  the object will travel infinite distance which is a portion of the circumference, if the object completed  two cycles the distance is the double the circumference.

3) An object starts from zero meters  and moves for instance toward 6  meters , if the deceleration increases infinitely opposing the object motion the distance traveled will increase without  bound but never reach the 6 meters distance.This idea is also represented in the special  theory of relatively in which a mass at motion increases in the speed but never reach the speed of light 3*10^8 m/s because the object's mass increases infinitely and the deceleration increases infinitely.

In all these cases the distance traveled for a mass  increases without bound and this what I mean by an infinite motion. The motion continuous non-stop
These are the only cases of a moving object that travels infinite distance and elapsing  infinite time non-stop

[Yahya A.Sharif (OP)]

Finite motion is when a mass moves from zero to reach a distance x meters in y seconds, when the object reaches this distance it will stop and while it is at stationary time elapses and it means the mass stopped at a time but did not continue any further meters while time passes . In contrary with the infinite motion time elapses while the mass is always moving

For an object to be at motion the distance it travels is always bigger than the previous distance In the three cases the distance increases:
1. 1,2,3......
2. quarter of the circumference in meters, half, the circumference, double the circumference in meters,......
3. 0.9,1,2,3,3.9999......,always less than 6 meters but infinite numbers

While the numbers are infinite the object will move non-stop and will be always at motion this means infinite motion.
The distance traveled is always bigger than the previous distance this means the object is always at motion whether it moves in a circle or boundary of 0 to 6" case 3 " and while the numbers between 0 to 6 are infinite " case 3" the motion will be infinite.

I can say that the three cases of infinite motion are motion within a boundary, motion  in a circle  and motion  in an open space.

[Kryptid]

The first type is sensible, but the second type probably isn't possible. The circular motion of an orbit, for example, doesn't last forever. At the very least, gravitational radiation would make that orbit decay over time. The third type would only be possible if space-time isn't quantized (which, honestly, we don't know whether it is or not).