Answer
$t=2.04s$
Work Step by Step
We can determine the required shortest time as follows:
According to Newton's second law
$\Sigma F_y=ma_y$
$\implies \Sigma F_y=m(0)=0$
$\implies N-W=0$
$\implies N=W=mg=10(9.81)=98.1N$
and $\Sigma F_x=ma_x$
$\implies \mu_s N=ma_x$
We plug in the known values to obtain:
$0.2\times 98.1=10a$
$\implies a=1.962m/s^2$
As $v=v_{\circ}+at$
We plug in the known values to obtain:
$4=0+1.962t$
This simplifies to:
$t=2.04s$
