Homework Help: What is the impulse of friction?

I was working on a basic momentum/impulse problem where a block is pushed by a force P over a time T that is plotted on a graph....Kinetic Friction is given but how would I incorporate that into the equation to find the velocity?

I know the impulse is the area under the curve....

[tex]mv_{1} + F_{avg}\Delta{t} = mv_{} [/tex]

 

Actually I figured it out, pretty easy...I just over thought it as usual....
This equation allowed me to come up with the correct answer

[tex] mv_{1} + P-T(\Delta{t}) = mv_{2}[/tex]

 

Im having trouble coming up with velocity for Time at 8 seconds.....I came up with the Velocity at 5 seconds easily using the equation above.....

heres the graph for the problem....http://img91.imageshack.us/img91/6935/graphmp3.jpg [Broken]


im trying to find the average Force at T = 8 seconds.....but its not working

 

I used this equation to solve for time at 5 seconds....and it worked...

[tex] mv_{1} + P-T(\Delta{t}) = mv_{2}[/tex]


but I tried solving for time at 8 seconds... finding the area under the curve which is just a rectange and triangle...but the answer comes up incorrect

as far as area it should just be [tex](L * W) + (.5*b*h)[/tex]