Can IR sensor detect the motion of a gun bullet or that is impossible ?!!
I doubt the typical hobby active IR sensor can do that. A PIR sensor certainly cannot. A higher end, professional IR sensor might be able to, but I couldn't say for certainty. A bullet's small size, speed, and even shape (round) are what make it hard to sense.
if you hit it right in the eye 
(sorry could not resist)
What is the approx speed of the bullet at moment of detection?
If the bullet flies 600km/hour = 170m/s and your camera can make 50 images per second
than the bullet flies 3 meter per image - will be very hard