Question

A bullet fired from a gun experience a force of 600 - 2 into 10 ki power 5t in the barrel of the gun here it is in 2nd the first become zero as soon as the bullet leave the barrel of the gun the time for with the bullet was in the barrel of the girl is

Answer 1

first we shall find the time taken by the bullet to come out of te barrel.
this will help us calculate the impulse on the bullet
the required time is 3*10 -3 s.
now we can calculate the impulse by two ways.
the first way is integration which is the most common method.
J = ∫F(t)dt = ∫{600-(2*10 5t)}dt
the limits shall be from t = 0 to t = 3*10 -3 s.
the other way is very simple. it is the method of average.
when a quantity has a linear variation we can take the average of the initial and final quantiites to evaluate such an integral
that is if F is a linear function of t then
∫ 0 T F(t)dt = <F(t)>T = {F(t = 0) + F(t = T)}/2.
both these ways give the same answer as 300 N-s.