Answer
$v=60.7ft/s$
Work Step by Step
We can determine the required velocity as follows:
First, we apply Newton's second law
$\Sigma F_y=0$
$\implies N-W=0$
$\implies N=W=10lb$
and $\Sigma F_x=ma_x$
$\implies F-\mu_k N=ma$
$\implies 8t^2-0.2(10)=\frac{10}{32.2}a$
This simplifies to:
$a=3.22(8t^2-2)$
We know that
$v-v_{\circ}=3.22(\frac{8}{3}t^3-2t)$
$\implies v=4+3.22(\frac{8}{3}t^3-2t)=8.587t^3-6.44t+4$.eq(1)
As $v=\frac{ds}{dt}=\int_o^t (8.587t^3-6.44t+4)dt$
$\implies s=2.147t^4-3.22t^2+4t$
This simplifies to:
$t=2.009s$
Now from eq(1), we obtain:
$v=8.58(2.009)^3-6.44(2.009)+4$
$\implies v=60.7ft/s$