Answer
$F=(7.85t+0.320)N$
Work Step by Step
We can determine the required force as follows:
$\Sigma F_s=m\frac{dv}{dt}+v_{D/i}\frac{dm_i}{dt}$
$\implies F-mgvt=0+v(mv)$
We plug in the known values to obtain:
$F=2(9.81)(0.4t+(0.4)^2)$
This simplifies to:
$F=(7.85t+0.320)N$
