Answer
$F=m^{\prime}v^2$
Work Step by Step
We can determine the required force as follows:
$\Sigma F_s=m\frac{dv}{dt}+\frac{dm_i}{dt}v_{D/i}$
As the car moves with constant speed,
$\frac{dv}{dt}=0$
$\implies F=(m_{\circ}-m^{\prime}v)(0)+v(m^{\prime}v)$
This simplifies to:
$F=m^{\prime}v^2$
