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Civil engineers use partial differential equations in many different situations. These include the following: heating and cooling; motion of a particle in a resisting medium; hanging cables; electric circuits; natural purification in a stream.
The question is pretty open ended. A number of mathematical (and related physics) concepts would be helpful for functioning as an astronaut. Motion of objects calcualtions need Trionometry/geometry and Algebra, for sure. Differential equations govern the motion as well. Do they need to be using them in space? Perhaps not directly, but it may become inherent in their experience.
u = initial velocity in newtons equations of motion.
Main application of rectilinear motion in the field of science is to find the motion, position and distance of an object. It can also be used to make comparison between the parameters of object in real field, relative velocity, relative motion and acceleration of an object can be determined. Thus, using the equations of rectilinear motion, one can take advantage in the field like factories of machinery where the terms like motion, acceleration, position of object are main functioning concern. Practically, to design something on the basis of motion, acceleration , etc , the equations of rectilinear motion are of great importance.
No. The equations for three or more bodies moving under the influence of each others' gravity, is extremely complex.