Step-by-step explanation:
From 0 to 334 m/s is average velocity of 167 m/s
so to travel the barrel length takes = .79 m / 167 m/s = .0047305 s
the is leads to acceleration of 334 m/ / .0047305 m/s = 70,605 m/s^2
F = ma
= .004 kg * 70 605 m/s^2 = 282 N