For #14 of the circular motion & rotation part of the AP style problems, for (c) why is the answer 2L/t instead of L/t? I don't understand why the L was doubled.

I'm assuming you're attempting to use v=d/t and coming up with L/t.  Recall, though, that this formula gives you AVERAGE velocity.

V_f is equal to 2*average velocity under constant acceleration, which you can provide by:

v_0=0

v=?

d=L

a

t=t

 

Solve vf^2=v_0^2+2ad to get v_f=Sqrt(2aL)

Solve d=v_o*t+.5*a*t^2 to get a=2L/t^2

Combine those two equations to eliminate a and solve for vf to show vf=Sqrt(4L^2/t^2)=2L/t