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.

 

[ogb p]

I would first clarify the units for the given force as they seem to be in N/s*t, which is not a standard unit for force. It is important to use consistent and accurate units in any scientific calculation.

Next, I would use the equation for linear momentum, p=mv, to find the initial momentum of the bullet. In this case, the initial momentum would be 0, as the bullet starts from rest.

Then, I would use the given force and the equation for impulse, J=F*t, to find the total linear impulse on the bullet. This impulse would be equal to the change in momentum of the bullet, which can be calculated as the final momentum (mv) minus the initial momentum (0).

Once the total linear impulse is known, I would use the equation for impulse again, but this time solving for time, to find the time it took for the bullet to leave the gun. It is important to note that there may be multiple roots for this equation, but only one of them would be physically meaningful. The correct root would be the one that yields a positive time value, as the bullet cannot leave the gun in negative time.

In conclusion, to find the total linear impulse on a bullet and the time it takes to leave the gun, one would need to use the equations for linear momentum and impulse, while also paying attention to consistent units and choosing the physically meaningful root for the equation.