a gun of mass M fires a bullet of mass m with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5sec is.

conservation of linear momentum

let the velocity of gun is V1 wrt earth

so velocity of bullet wrt eart is v-V1

m(v-v1) =Mv1

  v1=mv/(m+M)

now distance travel by gun in 0.5 sec

0=v1-a*0.5

a= 2v1     wher a is retardation of gun

so S= v1 *0.5 -1/2 *a *(0.5)²

       =v₁ /4

now from work energy theorem total work done is equal to change in kinetic energy

F.S =1/2 M *v1²    -0

F.v1 /4 = 1/2 M *v1²

F=2Mv1

  =2Mmv/(m+M)

Regards

Arun (askIITians forum expert)