Using Impulse to Solve For the Final Velocity

[spacestrudel]

Homework Statement

What is the final velocity of a bullet given that its change in time is 0.1 seconds and F(t) = Fc(1+e^(-1the00t). The mass of the bullet is 20g.

Relevant Equations

Mvf - mvo = change in p = the integral of Fdt

Hi there,

Just asking a logistics question since I want to be sure I am approaching this problem correctly.

My professor showed me an example of a bullet being fired from a barrel, given its initial velocity was 0. The change in time was 0.1 seconds. The mass of the bullet is 0.02 kg. The equation he gave is F(t) = F_c(1+e^(-100t)), where F_c = 100N.

Since we know that MV_f - MV₀ = Δp = ∫ Fdt, doesn't this mean I can set the given function equal to MV_f, since it is already force as a function of time (also since we know the initial velocity equals zero)? Or am I missing something?

Only asking because I can't tell if it's just a ridiculously easy problem or I'm missing something.

 

[haruspex]

doesn't this mean I can set the given function equal to MVf

You mean the integral of the function, right?

 

[spacestrudel]

You mean the integral of the function, right?

Does it still have to be the integral of that given function even though it is already in terms of F(t)? Because he said that the change in momentum was just the integral of F. So, since I have F(t) - isn't that technically the integral?

 

[haruspex]

Does it still have to be the integral of that given function even though it is already in terms of F(t)? Because he said that the change in momentum was just the integral of F. So, since I have F(t) - isn't that technically the integral?

No, what makes you think that? F(t) is the function, ∫F(t).dt is its integral. If F(t)=2t then its integral is t²+constant.

 

[spacestrudel]

No, what makes you think that? F(t) is the function, ∫F(t).dt is its integral. If F(t)=2t then its integral is t²+constant.

Got’cha! I don’t know, haha I was just taking the stuff he wrote on the board literally. Okay! So take the integral of the function given to then use to find the impulse ! Thank you.