Linear momentum acting on a bullet

[suspenc3]

I recently had a test question that gave a force acting on a bullet. The bullets mass is 0.016KG, and the force acting on the bullet is f=7000N-2.2*10^6N/s*t. The bullet is traveling 800 k/h when it leaves the gun

It asked to find the total linear impulse on the bullet, and then how much time it took to leave the gun.

L1+IMP=L2
L1 is zero since zero initial velocity

f*t=m*vf

this gives a quadratic only unknown is t

how do I know which root is correct?

BTW the two I get are 0.000633 s and 0.0025 s

 

[Dick]

Once you have the total impulse, don't you want to just integrate f(t)dt and set that equal to the total impulse? You can't just take force times time. The force isn't constant.