It is important first to note that t he block will not move until the force is large enough to overcome static friction. Thus, the exact time the box first moves needs to be determined.
The block will move when the force is equal to friction force to move. Summing the forces in the x-direction, gives,
25 t0.5 - f = 0
μN = 25 t0.5
0.25 (100) = 25 t0.5
t = 1.0 s
The motion of the box will depend on the linear impulse between 1 and 2 seconds.
(1.8856 - 2) - (0.6667 - 1) = 0.1242 v2
v2 = 1.763 ft/s