  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.
