Block Movement Dynamics: Solving for Time, Acceleration, and Distance

[Preach99]

Homework Statement

Hi guys. First of all, great forum you've got here.

I have a problem and I hope you can help me with this one.

Block of mass m lies on a rough horizontal surface. In the period 0 - t1, the block is moving due to the force F(t), which varies depending on the time. In period t1 - t2 we only have friction (F=0), and the block in the time t2 has speed v2=1 m/s. I have to find time t2, acceleration in t2 (a2) and distance s2. I also have to draw a, v, t diagrams.

Homework Equations

m2v⃗ -m1v⃗ 1=∫F(t)⃗ dt

The Attempt at a Solution

my formula in mathcad

I'm stuck with this integration. I understand that the first part (F*cos(60°)) is the area under the curve - √2 *m*g

I hope you guys can help. Thank you in advance.

 

[Preach99]

wow, 400 views and no reply lol

I was quite busy today but I tried a different approach.
First, I only calculated the part from 0 to t1 with that Impulse formula and the speed v1 (@ t1) is 4.346 m/s.

Then, since the force is F=0, I have Fn=m*g (y axis), and Frx=-μ*m*g (x axis).
And when I try to calculate this part, I get a weird result -> t2=0.394 s lol.
IDK, this could only make sense if the real t2 time would be √2+0.394=1.808 seconds