Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as 8.00 x 10⁶ m/s. These techniques allow a much more favorable payload-to-fuel ratio. To illustrate this fact: 

(a) Calculate the increase in velocity of a 20,000-kg space probe that expels only 40.0-kg of its mass at the given exhaust velocity. 

(b) These engines are usually designed to produce a very small thrust for a very long time-the type of engine that might be useful on a trip to the outer planets, for example. Calculate the acceleration of such an engine if it expels 4.50 x 10^-6 kg/s at the given velocity, assuming the acceleration due to gravity is negligible.