A spaceship with a thruster - one body, one force
  A spaceship with one thruster producing a constant magnitude force is analyzed for various initial conditions. This elementary problem, with one object acted upon by one force, has value as a challenge to one's physical intuition and in demonstrating the benefits and limitations of dimensional analysis. In addition, the problem can serve to introduce a student to special functions, provide a mechanical model for Fresnel integrals and the associated Cornu spiral, or be used as an example in a numerical methods course. The problem has some interesting and perhaps unexpected features. 
Scott C. Dudley and Mario A. Serna