In Chapter 47.5 of Bungou Stray Dogs, Atsushi manages to catch a bullet in his mouth. One of the most impressive things about this feat though, is that he didn't actually notice the bullet until it was a few centimetres from his face.
Fig 1
Fig 2
Distance between Atsushi and the Bullet[]
So, images. In Fig 1, Atsushi notices the bullet. Based on lengths of bullets and the size of his face, I think it's reasonable to say there is a distance of 4 - 5 cm between the bullet and Atsushi. (0.04 / 0.05 m)
Bullet Speeds[]
Now, how fast is the bullet? Unfortunately, I could not find any bullet velocities specifically for SMG bullets (sue me, there's a lot of different types of SMGs and bullets) so I'll just be using some low, mid and high ends of bullet speeds.
Low End - speed of a slow shotgun pellet = 335m/s. Info from the Physics Factbook.
Mid End - average speed of a bullet = 2,500 feet per second = 762m/s. Info from Mythbusters
High End - bullet from a .220 Swift Rifle = 4,000 feet per /s = 1,200 m/s. Info from Wikipedia
Reaction Speed[]
So, how much time does our furry friend have to react then?
Using the equation, time = Distance / Speed, we find that:
Low End (5cm distance)
T = 0.05m/335m/s
= 0.00014925373 of a second = 149.253731 microseconds => Hypersonic+ reactions
Mid End (5cm distance)
T = 0.05m/762m/s
= 0.00006561679 of a second = 65.6167979 microseconds => High Hypersonic+ reactions
High End (5cm distance)
T = 0.05m/1,200 m/s
= 0.00004166666 of a second = 41.6666667 microseconds => High Hypersonic+ reactions
Low End (4cm distance)
T = 0.04m/335m/s
= 0.00011940298 of a second = 119.402985 microseconds => High Hypersonic
Mid End (4cm distance)
T = 0.04m/762m/s
= 0.00005249343 of a second = 52.4934383 microseconds => High Hypersonic+ reactions
High End (4cm distance)
T = 0.04m/1,200 m/s
= 0.00003333333 of a second = 33.3333333 microseconds => High Hypersonic+ reactions
Further Information (Edit)[]
Fig 3
Fig 3 shows the type of guns used. Based on their appearances, they are likely OTs-02 Kiparis (credit to Unite My Rice for the find).
This would place the speed of the bullet Atsushi dodged at 340m/s, so just over the low ends used.
Conclusions[]
Atsushi's reaction perception speeds and reaction speeds are likely Hypersonic+ to High Hypersonic
Final Thoughts[]
Atushi was sprinting towards the bullet at high speeds when this happened, so relative to him, the bullet would have actually been moving even faster, and thus his reactions would actually be higher than what is calculated here. However, I can't use his speed on top, as that would be calc stacking unfortunately