Answer
$v=59.8ft/s$
Work Step by Step
We can determine the velocity of the block as
$\Sigma F_y=0$
$\implies N-W=0$
$\implies N=W=10lb$
and $\sigma F_x=ma_x$
$\implies F-\mu_k N=ma$
We plug in the known values to obtain:
$8t^2-(0.2)(10)=\frac{10}{32.2}a$
This simplifies to:
$a=3.22(8t^2-2)$
We know that
$a=\frac{dv}{dt}=\int_0^t 3.22(8t^2-2)dt$
$\implies v-v_{\circ}=3.22(\frac{8t^3}{3}-2t)$
$\implies v=4+3.22[\frac{8}{3}(2)^3-2(2)]$
$\implies v=59.8ft/s$
