Chapter 15 - Kinetics of a Particle: Impulse and Momentum - Section 15.9 - Propulsion with Variable Mass - Problems - Page 312: 145

$a=0.0476m/s^2$

We can determine the required acceleration as follows: $\Sigma F_s=m\frac{dv}{dt}-v_{D/e}\frac{dm_e}{dt}$ We plug in the known values to obtain: $0=(10\times 10^3+500)a-(10)(50)$ This simplifies to: $a=0.0476m/s^2$